The final verdict

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The final verdict Anonymous Fri Dec 4 07:56:56 2020 No.12418876 [Reply] [Original]

There are 3 possible scenarios:
1. There are 2 heads coins
2. There is a heads coin and a tails coin
3. There are 2 tails coins
Next we eliminate those which dont fit the criteria of having "at least one coin is heads" and we are left with:
1. There are 2 heads coins
OR
2. There is a heads coin and a tails coin
The question does not give any information regarding order of the coins, therefore there is no "first" or "second" coin, there are only the sets which contain either 2 heads or a heads and a tails.
Probability= favourable outcomes/possible outcomes
Without the criteria of "at least one is heads" there would be 3 possible outcomes, and a 1/3 chance of both being heads, but after applying that criteria, it becomes impossible to land two tails coins. Thus we are left with one favourable outcome (both coins are heads) and two possible outcomes (both are heads OR one heads and one tails)
The probability of both coins being heads is 1/2

>>	Anonymous Fri Dec 4 07:59:56 2020 No.12418883 Is this your or Bob’s opinion?

>>	Anonymous Fri Dec 4 08:00:45 2020 No.12418889 >>12418876 Are you mentally ill?

>>	Anonymous Fri Dec 4 08:10:28 2020 No.12418908 >>12418876 Couldn't this be found out empirically with a few hundred coin tosses?

>>	Anonymous Fri Dec 4 08:11:35 2020 No.12418909 >>12418876 Two coins [math]\Rightarrow [/math] two random variables. The coins are indexed. Probability is 1/3.

>>	Anonymous Fri Dec 4 08:24:43 2020 No.12418931 >>12418909 Without any information about the distribution, we should assume a flat prior. Thus two heads is as likely as a head and tails. This is standard textbook probability theory.

>>	Anonymous Fri Dec 4 08:26:30 2020 No.12418936 >>12418909 >Two coins two random variables two random variables that will randomly land on scenarios within the bounds of the criteria. >Probability is 1/3. Show me 3 possible outcomes that fit the criteria of "at least one is heads"

>>	Anonymous Fri Dec 4 08:27:38 2020 No.12418940 >>12418936 HH, HT, TH

>>	Anonymous Fri Dec 4 08:31:04 2020 No.12418947 >>12418940 HT and TH are both exactly the same, as they both contain one heads coin and one tails coin. there is no first or second coin and the problem gives no information about the order of the coins. They are both one heads and one tails

Anonymous Fri Dec 4 08:39:25 2020 No.12418962

>>12418947
Any two coins are distinguishable. The random variables corresponding to each coin are therefore independent. Therefore, HT and TH are distinct.
Alternatively, if you wish to HT and TH as identical, then HT \mapsto 1/2, while HH \mapsto 1/4, and TT \mapsto 1/4. After removing TT and normalizing, you see that HT \mapsto 2/3 and HH \mapsto 1/3.

>>	Anonymous Fri Dec 4 08:47:51 2020 No.12418974 >>12418962 You're forgetting that two heads makes it twice as likely that "at least one is heads" is given as information. So HH is as likely as HT or TH and the answer remains 1/2.

>>	Anonymous Fri Dec 4 08:48:57 2020 No.12418976 >>12418947 you flip two coins. what is the probability that both are head?

>>	Anonymous Fri Dec 4 08:51:34 2020 No.12418983 >>12418931 >Without any information about the distribution, we should assume a flat prior. that's clearly wrong, heuristically

>>	Anonymous Fri Dec 4 08:52:50 2020 No.12418987 >>12418974 >You're forgetting that two heads makes it twice as likely that "at least one is heads" is given as information Prove it then.

Anonymous Fri Dec 4 08:54:25 2020 No.12418991

>>12418962
>HT \mapsto 1/2, while HH \mapsto 1/4, and TT \mapsto 1/4. After removing TT and normalizing, you see that HT \mapsto 2/3 and HH \mapsto 1/3.
if it is the case that any two coins are distinguishable then i can just as easily say that h refers to a second heads coin (if present in the set) and divide HH into Hh and hH to distinguish them, bringing the probability back to 1/2
These things will only matter if the coins are flipped one after the other and there is a first and second coin, which the problem didnt specify.

>>	Anonymous Fri Dec 4 08:54:50 2020 No.12418994 >>12418983 How so?

>>	Anonymous Fri Dec 4 08:56:09 2020 No.12418995 >come to /sci/ to see what it's like >they're arguing over 5th grade math

>>	Anonymous Fri Dec 4 08:57:03 2020 No.12418996 >>12418994 flip two coins several times. you will see that HT occurs more frequently than HH.

Anonymous Fri Dec 4 08:58:54 2020 No.12418997

>>12418991
No, because in that case H is in the domain of the first random variable but not the second random variable, while h is in the domain of the second random variable but not the first random variable, so only one of Hh or hH is an outcome of the system.

>>	Anonymous Fri Dec 4 08:59:03 2020 No.12418998 >>12418987 the probability of one of the coins being heads is 100% if we look at them as separate entities. If this wasnt true, then getting TT would be a possibility, which it isnt.

Anonymous Fri Dec 4 09:01:01 2020 No.12419001

>>12418987
Sure. Since coins are distinguishable there are four coins that can be given as heads:

1. two heads are tossed, left coin is given as "at least one is heads"

2. two heads are tossed, right coin is given as "at least one is heads"

3. Right coin is heads and left is tails

4. Left coin is heads and right is tails

Half of the time "at least one is heads" both are heads.

>>	Anonymous Fri Dec 4 09:01:26 2020 No.12419002 >>12418908 every time this thread pops up, a different anon codes a script and shows that the probability converges to 1/3. Trolls will never ever stop posting this shit though, it's a /sci/ meme.

Anonymous Fri Dec 4 09:02:10 2020 No.12419005
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LMFAO YES!
In this thread "boy girl" schizo foams at the mouth for 500 comments about a wikipedia psychoanalysis of ambiguous language, and how it is somehow related to the unambiguous language in the OP question.

Boy girl schizo unfortunately loses 0-500 yet again, but the award for best supporting actor will almost certain be won by his imaginary friend, Bob.

>>	Anonymous Fri Dec 4 09:02:12 2020 No.12419006 >>12418996 Which coins though? The distribution is unknown.

>>	Anonymous Fri Dec 4 09:03:11 2020 No.12419009 >>12419001 >left coin is given as "at least one is heads" >right coin is given as "at least one is heads" Never happens.

>>	Anonymous Fri Dec 4 09:03:23 2020 No.12419010 >>12419001 you're assuming that a specific coin is given as heads. that's not what the problem says. it's an information about both coins which cannot be reduced to an information about a single coin.

Anonymous Fri Dec 4 09:05:20 2020 No.12419017

>>12418996
>>12419002
Yes that is true because in the real world there will always be a first and second coin, and the probability would definitely be 1/3. The problem however doesnt mark any coin as "coin 1" or "coin 2", so changing the order of the coins doesnt change what is contained in the set. Without marking the coins, show me 3 possible outcomes other than two heads and one heads one tails

>>	Anonymous Fri Dec 4 09:08:44 2020 No.12419026 >>12419006 This exactly. You cannot say that TH and HT are distinguished from one another and HH is one result when HH consists of 2 different distinguished random entities.

Anonymous Fri Dec 4 09:09:03 2020 No.12419028

>>12419017
it doesn't matter if you work with ordered or unordered coin tosses.

with ordered tosses, the sample space is {HH,TH,HT,TT} with uniform distribution.

with unordered tosses, the sample space is {HH,TH,TT} where the distribution is

P(TH) = 1/2
P(HH) = P(TT) = 1/4

probability of both heads with the assumption that TT cannot occur is 1/3 in both cases.

>>	Anonymous Fri Dec 4 09:09:34 2020 No.12419029 >>12419017 >show me 3 possible outcomes There aren't, and one each happens twice as often. x + 2x = 1 3x = 1 x = 1/3 HH = 1/3 HT = 2/3 ezpz

Anonymous Fri Dec 4 09:09:49 2020 No.12419030

>>12419017

import scipy.stats

I = 100000 # number of tosses

Tosses_with_at_least_one_head = 0
Tosses_with_both_heads = 0

for k in range(0,I):
toss = scipy.stats.bernoulli.rvs(size=2,p=1/2)
if sum(toss) >= 1:
Tosses_with_at_least_one_head += 1
if sum(toss) == 2:
Tosses_with_both_heads +=1

P = Tosses_with_both_heads/Tosses_with_at_least_one_head
print(P)

this script does not index the coins. It converges to 1/3

>>	Anonymous Fri Dec 4 09:10:05 2020 No.12419034 >>12419026 >HH is one result when HH consists of 2 different distinguished random entities. now you're just being retarded on purpose

>>	Anonymous Fri Dec 4 09:10:30 2020 No.12419037 >>12419017 If you toss two coins HH will show 1/4 of times, HT 2/4 and TT 1/4. If you remove TT you are left with HH 1/4 and HT 2/4.

>>	Anonymous Fri Dec 4 09:12:05 2020 No.12419039 >>12419001 This is the most nonsensical argument I've ever seen on this topic.

>>	Anonymous Fri Dec 4 09:18:19 2020 No.12419050 File: 100 KB, 700x70, output_2.webm [View same] [iqdb] [saucenao] [google] Why are we even talking about this

>>	Anonymous Fri Dec 4 09:21:28 2020 No.12419058 >>12419028 >>12419029 >>12419030 >>12419034 >>12419037 I accept defeat, and i concede that the probability is in fact 1/3, thank you for opening my eyes.

>>	Anonymous Fri Dec 4 09:21:30 2020 No.12419059 >>12419050 >Why are we even talking about this some people are hallucinating

>>	Anonymous Fri Dec 4 09:22:46 2020 No.12419063 >>12419039 If you think that's good, just wait for the follow-up argument, which constructs an imaginary friend Bob, who can then enter the question in order to "observe" and "know" specific coins, and then relay that knowledge back to the test taker.

>>	Anonymous Fri Dec 4 09:25:17 2020 No.12419071 >>12419009 So the answer is 0?

>>	Anonymous Fri Dec 4 09:26:42 2020 No.12419076 >>12419071 Neither the left nor the right coin are ever given as heads.

Anonymous Fri Dec 4 09:27:36 2020 No.12419079

>>12419010
>you're assuming that a specific coin is given as heads.
Please explain how "at least one is heads" doesn't mean a coin is heads.

>it's an information about both coins
No, it's information about one. Assuming it's information about both is adding information not given and fails to treat the coins as distinguishable objects.

>>	Anonymous Fri Dec 4 09:27:38 2020 No.12419080 >>12418876 >your head is a coin >on both sides, what is the chance that this happens

>>	Anonymous Fri Dec 4 09:28:42 2020 No.12419086 >>12419039 Do you have an actual argument against it?

>>	Anonymous Fri Dec 4 09:30:06 2020 No.12419091 >>12419079 >Please explain how "at least one is heads" doesn't mean a coin is heads. Read the question, it refers to the result of two coin flips, not to one coin.

>>	Anonymous Fri Dec 4 09:32:20 2020 No.12419095 >>12419079 >No, it's information about one. Did Bob tell you that? I couldn't find it in the OP

Anonymous Fri Dec 4 09:32:34 2020 No.12419097

>>12419076
It's not clear what you mean. Do you mean it's not specified whether the coin referred to is the left or right coin? That has no bearing on my argument since it allows either coin to be the one referred to. Do you mean neither coin is heads? Then how is at least one heads?

Anonymous Fri Dec 4 09:33:10 2020 No.12419099

>>12419086
>left coin is given as "at least one is heads"
>right coin is given as "at least one is heads"
This doesn't even make sense in the context of the question. The condition is just that "at least one coin is heads". Also, this condition that at least one coin is heads does not change the fact that the probability of one heads and one tails is twice that of the probability that both coins are heads.

>>	Anonymous Fri Dec 4 09:34:14 2020 No.12419100 >>12419079 consider [math](x_1,y_2) \in \mathbb{R}^2[/math]. is "at least one coordinate is non-zero" information about both coordinates, or can it be reduced to an information about a single coordinate?

>>	Anonymous Fri Dec 4 09:34:38 2020 No.12419101 >>12419097 There is no coin that is ever "the one referred to."

>>	Anonymous Fri Dec 4 09:37:02 2020 No.12419107 >>12419091 That doesn't follow. "At least one is heads" refers to "one" coin, among two.

Anonymous Fri Dec 4 09:40:48 2020 No.12419120

>>12419107
No. It is a statement about the system (which involves two coins). Labeling the coins A and B, we see that the statement "there is at least one heads" depends on the state of both A and B. Why? If A is not heads, then the statement depends on the state of B. On the other hand, if B is not heads, then the statement depends on A. Therefore, the statement "there is at least one heads" cannot be fully determined by looking at the outcome of only one of the coins.

>>	Anonymous Fri Dec 4 09:41:23 2020 No.12419121 >>12419095 >at least one is heads

>>	Anonymous Fri Dec 4 09:41:34 2020 No.12419123 >>12419107 No, the second clause in the sentence refers directly to the first clause, not to something else.

>>	Anonymous Fri Dec 4 09:42:36 2020 No.12419132 >>12419121 >at least one [ref. "You flip two coins"] is heads

>>	Anonymous Fri Dec 4 09:42:42 2020 No.12419133 >>12419099 >The condition is just that "at least one coin is heads" Right, which means one coin is heads. Either the left coin or the right coin. It's not that hard, you'll get it eventually.

>>	Anonymous Fri Dec 4 09:43:03 2020 No.12419135 >>12419107 no. it's an information about both coins. just because it uses the word "one" doesn't mean it's an information about a single coin.

>>	Anonymous Fri Dec 4 09:44:28 2020 No.12419141 >>12419133 >Either the left coin or the right coin. Did Bob tell you this? I couldn't find it in the OP

>>	Anonymous Fri Dec 4 09:45:33 2020 No.12419144 >>12419101 >There is no coin that is ever "the one referred to." So there is no coin that is heads? No, clearly that information is given.

>>	Anonymous Fri Dec 4 09:46:25 2020 No.12419146 >>12419144 One of the two coin flips resulted in heads.

Anonymous Fri Dec 4 09:49:08 2020 No.12419152

>>12419120
>No. It is a statement about the system (which involves two coins).
Right, a statement about one coin is also a statement about the system.

>Labeling the coins A and B, we see that the statement "there is at least one heads" depends on the state of both A and B. Why? If A is not heads, then the statement depends on the state of B. On the other hand, if B is not heads, then the statement depends on A.
That's exactly what I showed here >>12419001. Do you have an actual point?

>Therefore, the statement "there is at least one heads" cannot be fully determined by looking at the outcome of only one of the coins.
Who is determining it or looking at the outcome? The information is given. Stop hallucinating, schizo.

>>	Anonymous Fri Dec 4 09:49:13 2020 No.12419153 >>12419144 There are two coin flips, which resulted in one or more heads.

>>	Anonymous Fri Dec 4 09:51:00 2020 No.12419156 >>12419152 >Who is determining it or looking at the outcome? Bob is, apparently. The OP certainly isn't.

>>	Anonymous Fri Dec 4 09:54:49 2020 No.12419173 >>12419100 Clearly it's only telling you about one coordinate, not both. Saying it's about both is fake information you don't have. I'm not sure what you mean by "reduced" to since saying one coordinate is non-zero is already about a single coordinate.

>>	Anonymous Fri Dec 4 09:56:18 2020 No.12419179 >>12419173 >one coordinate is non-zero is already about a single coordinate That statement refers to two coordinates, not to a single cooridnate.

>>	Anonymous Fri Dec 4 09:58:14 2020 No.12419184 >>12419123 Where did I say anything different? If course is referring to one coin among the pair previously referred to, not some other coin.

>>	Anonymous Fri Dec 4 09:58:22 2020 No.12419185 >>12419173 >saying one coordinate is non-zero is already about a single coordinate That statement refers to two coordinates, not to a single coordinate.

>>	Anonymous Fri Dec 4 09:58:49 2020 No.12419189 >>12419173 >>12419173 consider [math](x_1,y_2) \in \mathbb{R}^2[/math]. is "[math]x^2+y^2 > 0[/math]" information about both coordinates, or can it be reduced to an information about a single coordinate?

>>	Anonymous Fri Dec 4 09:59:16 2020 No.12419192 >>12419132 And?

>>	Anonymous Fri Dec 4 09:59:25 2020 No.12419193 >>12419184 It's referring directly to two coin flips, not to one coin.

>>	Anonymous Fri Dec 4 09:59:52 2020 No.12419195 >>12419189 [math](x_1,y_2) = (x,y)[/math], my bad

>>	Anonymous Fri Dec 4 10:00:34 2020 No.12419198 >>12419192 The reference is to the first clause of the sentence, not to something else.

>>	Anonymous Fri Dec 4 10:01:47 2020 No.12419202 >>12419135 >it's an information about both coins. >one is not >both are Trying to stretch information about one coin to both coins is just making up fake information.

>>	Anonymous Fri Dec 4 10:02:31 2020 No.12419205 >>12419202 There is no information that refers to a single coin.

>>	Anonymous Fri Dec 4 10:03:17 2020 No.12419208 >>12419202 it already is an information about both coins

>>	Anonymous Fri Dec 4 11:05:16 2020 No.12419385 File: 48 KB, 469x547, 2020-11-30 (1).png [View same] [iqdb] [saucenao] [google] >>12418908 >>12418931 >>12418987 >>12419006

>>	Anonymous Fri Dec 4 11:06:39 2020 No.12419388 >>12419058 Wow, some actual humility on /sci/, truly a sight to behold. Very based anon

>>	Anonymous Fri Dec 4 11:09:45 2020 No.12419405 >>12419107 Can be said about two coins too. X the number of coins that are heads X = 2 -> X ≥ 1 https://mathworld.wolfram.com/AtLeastOne.html

>>	Anonymous Fri Dec 4 11:09:52 2020 No.12419406 >>12419385 Why'd you tag me? The result is 1/3, as I said.

>>	Anonymous Fri Dec 4 11:11:59 2020 No.12419416 >>12419202 Trying to reduce an unspecified number of coins to only one is just making up fake information.

>>	Anonymous Fri Dec 4 11:13:57 2020 No.12419418 >>12419406 meant to tag the dude you were tagging, all good anon

Anonymous Fri Dec 4 11:25:44 2020 No.12419459

>>12419173
>I'm not sure what you mean by "reduced"
there's a predicate [math]P(x)[/math] defined for [math]x \in \mathbb{R}[/math] such that either

"at least one coordinate is non-zero" [math]\iff P(x_1)[/math]

or

"at least one coordinate is non-zero" [math]\iff P(x_2)[/math]

there isn't. "at least one coordinate is non-zero" depends on both coordinates, and therefore cannot be described as an information about a single coordinate. it's counter intuitive, but true nonetheless.

>>	Anonymous Fri Dec 4 11:33:01 2020 No.12419486 Jesus fucking christ you guys are retarded: Hh hH Ht tH It’s 1/2 idiots

>>	Anonymous Fri Dec 4 11:39:51 2020 No.12419504 >>12419486 What do H,h and t correspond to? Last time I checked, a coin has two sides.

Anonymous Fri Dec 4 11:49:53 2020 No.12419543

>>12419504
If you had any sentience you would understand that H is the coin that has already been determined to be heads. It is not surprising a malformed flourided clamped spaded sub-hominid as yourself would not draw any meaningful inference. Did you know coins can actually land neither heads or tails?

>>	Anonymous Fri Dec 4 11:51:23 2020 No.12419551 >>12419543 >the coin that has already been determined to be heads >the coin into the trash it goes

>>	Anonymous Fri Dec 4 12:01:39 2020 No.12419576 >>12419504 Looks like a coded message from Bob. Any cryptography experts in here?

>>	Anonymous Fri Dec 4 13:37:16 2020 No.12419850 >>12419153 Right, meaning one coin is heads.

>>	Anonymous Fri Dec 4 13:38:25 2020 No.12419853 >>12419185 No it refers to one coordinate being non-zero.

>>	Anonymous Fri Dec 4 13:39:44 2020 No.12419857 >>12419850 No, it means what it says. There are two coin flips, which resulted in one or more heads.

>>	Anonymous Fri Dec 4 13:41:09 2020 No.12419860 >>12419853 No, it also means what it says, not something else.

>>	Anonymous Fri Dec 4 13:46:25 2020 No.12419883 (X ≥ 1) = (X = 1) ∪ (X = 2)

>>	Anonymous Fri Dec 4 14:04:47 2020 No.12419934 >>12419853 No, that also means what it says, not something else.

>>	Anonymous Fri Dec 4 14:11:52 2020 No.12419946 >>12419853 It refers to a certain number of coins that are heads, a number that is not zero.

>>	Anonymous Fri Dec 4 14:58:44 2020 No.12420041 >>12419946 This is logically equivalent to saying (A & (B V!B)) v (B & (A v !A)) By reduction A v B Really straightforward.

>>	Anonymous Fri Dec 4 14:59:58 2020 No.12420044 >>12420041 Cool, another coded message from Bob.

>>	Anonymous Fri Dec 4 15:49:32 2020 No.12420164 File: 880 KB, 745x817, 1490383170344.png [View same] [iqdb] [saucenao] [google] Let's go boy girl schizo! RAH ! RAH !! RAH !!! Don't let me down, you worm brained retard, I paid good money for these tickets. Hh hH Ht tH hH Ht tH

>>	Anonymous Fri Dec 4 15:53:55 2020 No.12420173 OP is right. It’s 1/2.

>>	Anonymous Fri Dec 4 15:57:17 2020 No.12420178 >>12420173 YAAASSSS QUEEEEEN

>>	Anonymous Fri Dec 4 16:20:37 2020 No.12420223 >>12420041 >>12419883 hon hon hon tit croissant

Anonymous Fri Dec 4 16:37:05 2020 No.12420263

>>12418931
>Without any information about the distribution
"You flip two coins" is that information.

Perhaps the wording is misleading. If you phrase it using the past tense, it's more obvious: "Of all trials where two coins are flipped and those trials where both coins come up tails are discarded, what fraction of the remaining trials are both heads." When it is worded like this, then the answer is obviously 1/3rd.

Anonymous Fri Dec 4 17:06:16 2020 No.12420329

>>12420263
>"Of all trials where two coins are flipped and those trials where both coins come up tails are discarded, what fraction of the remaining trials are both heads."
I disagree. Your new wording is actually less clear than the original wording, which is not only perfectly clear, but also doesn't confuse the reader by taking the form of a run-on sentence, or by referring the reader to an unspecified number of trials, some of which are discarded.

But yes, the answers to both are obviously 1/3.

>>	sinenomine Fri Dec 4 17:09:32 2020 No.12420335 >>12418876 nobody thought about the second coin standing on it's edge

Anonymous Fri Dec 4 17:27:16 2020 No.12420398

>>12420263
>Of all trials where two coins are flipped and those trials where both coins come up tails are discarded, what fraction of the remaining trials are both heads.
it's fun that we know an information about every pair in the remaining set of trials: at least of the coins is heads. and yet it doesn't imply that we know the value of only one coin in the pair, or that a coin has been "observed".

I wonder where will this take us.

>>	Anonymous Fri Dec 4 17:34:19 2020 No.12420422 File: 13 KB, 800x600, Cointism.png [View same] [iqdb] [saucenao] [google] Is theres something im missing? is this bait? its 1/3. each square has an equal chance (25%) of occurring. with TT removed the options are HT, TH, and HH. So 1/3.

>>	Anonymous Fri Dec 4 17:36:52 2020 No.12420427 >>12420422 >Is theres something im missing? is this bait? welcome to the loony bin. people are legit hallucinating in this thread.

>>	Anonymous Fri Dec 4 17:50:30 2020 No.12420465 >>12420398 > I wonder where will this take us. To a completely different problem, with a whole new multiverse of Bob clones who are all playing a game of thrones against themselves and the test taker.

>>	Anonymous Fri Dec 4 20:33:05 2020 No.12420953 >>12419405 Right, and how does that respond to anything I said?

>>	Anonymous Fri Dec 4 20:34:08 2020 No.12420955 >>12419198 Yeah, and?

>>	Anonymous Fri Dec 4 20:36:44 2020 No.12420968 >>12419189 Information about both.

>>	Anonymous Fri Dec 4 20:37:45 2020 No.12420974 >>12419193 Is referring to a coin flip in the pair being heads.

>>	Anonymous Fri Dec 4 20:38:48 2020 No.12420979 >>12419205 "At least one is heads" >>12419208 No.

>>	Anonymous Fri Dec 4 20:39:50 2020 No.12420985 >>12419385 That's nice, now do the problem.

>>	Anonymous Fri Dec 4 20:40:56 2020 No.12420989 >>12419416 >Trying to reduce an unspecified number of coins An unspecified number is not information, one coin being heads is information.

Anonymous Fri Dec 4 20:44:01 2020 No.12420999

>>12419459
>"at least one coordinate is non-zero" depends on both coordinates
Depends on in what way? As in, you need to check both coins to determine whether it's true? That's competent irrelevant and backwards. We are already given the information that it's true.

>>	Anonymous Fri Dec 4 20:45:23 2020 No.12421004 >>12419857 >>>12419934 >No, it means what it says. So you agree I'm right, good.

>>	Anonymous Fri Dec 4 20:47:02 2020 No.12421009 >>12419946 >It refers to a certain number of coins that are heads, a number that is not zero. No, you're talking about coordinates, and a number that isn't zero is not the same thing as at least one.

Anonymous Fri Dec 4 20:50:37 2020 No.12421023

>>12418876
get two coins, toss both at the same time, record if there are 1 head or 2. If there are 0 heads record nothing and flip again until you record either 1 head or 2. Do this 100 times and tell us how many times there are 2 heads. Maybe then you can stop making this thread you utter fucking moron.

Anonymous Fri Dec 4 20:56:59 2020 No.12421037

>>12420263
>"You flip two coins" is that information.
Sure, but not about the distribution of two coin flips.

>Of all trials where two coins are flipped and those trials where both coins come up tails are discarded
Incorrect, it should be of all coins where a head is observed, how many are part of a pair of heads. It's very simple.

Anonymous Fri Dec 4 21:43:34 2020 No.12421158

This is not true. Let's say that you clip the coins simultaneously and they land a foot apart. You can only view one at a time. You know that each individual chance that it turns heads is 1/2.

The chance that it turns heads twice is 1/4, because no matter what these coins are not fluid and are separate entities. The number of possibilities is not 3, as the coins are independent entities and saying that one is heads and the other is tails is only half of the possibilities, as each could be inverse and it would still be true

Anonymous Fri Dec 4 22:40:39 2020 No.12421302

<?php
// Copyright 2020 - Pajeet Sandeep
// 5+ year experience, graduate from University of New Delhi
// Written in PHP programming language

define("HEADS", 1);
define("TAILS", 0);

// This array to store valid tosses
$total_tosses_at_least_one_head = array();

// This array to store tosses double head
$total_both_heads = array();
for($i = 0; $i < 100000; $i++){
// Flip coins 1
$coin1 = mt_rand(0,1);

// Flipping coining 2
$coin2 = mt_rand(0,1);

// Test if coining 1 is head
if ($coin1 != TAILS && $coin1 == HEADS){

// This would be valid tossing so append to array
$total_tosses_at_least_one_head[] = mt_rand(0, mt_getrandmax());

// The first coining is heads, now lets test second coining!
if ($coin2 != TAILS && $coin2 == HEADS){
// The second coins is head!
// Append a random number to array
$total_both_heads[] = mt_rand(0, mt_getrandmax());
}
}

// Test if second coining is not tailing
if ($coin2 != TAILS && $coin2 == HEADS){

// This would be valid tossing so append to array
$total_tosses_at_least_one_head[] = mt_rand(0, mt_getrandmax());

// The second coining is heads, now lets test the first coining
if ($coin1 != TAILS && $coin1 == HEADS){
// The first coins is head as well!
// Append a random number to array
$total_both_heads[] = mt_rand(0, mt_getrandmax());
}
}

// If both of the coinings are HEAD then we need to remove 1 result!
if ($coin1 == HEADS && $coin2 == HEADS){
// Remove some elements from arrays!!
array_pop($total_both_heads);
array_pop($total_tosses_at_least_one_head);
}
}

// Count the elements in the arrayings and display on the computer screen
echo count($total_both_heads) / count($total_tosses_at_least_one_head);

// Result = 0.33518755669388
?>

>>	Anonymous Sat Dec 5 01:37:55 2020 No.12421709 >>12420953 >"At least one is heads" refers to "one" coin, among two. "At least one is heads" refers to a number of coins among two that is not zero. {1, 2}

>>	Anonymous Sat Dec 5 01:42:45 2020 No.12421720 >>12420989 One coins being heads, OR two coins being heads. X ≤ 2 ∪ X ≥ 1 = (X = 1) ∪ (X = 2) X = {1, 2} You have to consider both cases

>>	Anonymous Sat Dec 5 01:46:10 2020 No.12421734 >>12421009 >a number that isn't zero is not the same thing as at least one. Considering we are dealing with natural numbers given positive discrete values, yes, it is the same.

>>	Anonymous Sat Dec 5 01:49:38 2020 No.12421742 >>12421302 based pajeet

>>	Anonymous Sat Dec 5 01:57:33 2020 No.12421758 File: 3 KB, 132x188, Untitled.png [View same] [iqdb] [saucenao] [google] wouldn't it just be 50; same as one coin flip?

>>	Anonymous Sat Dec 5 01:58:35 2020 No.12421759 File: 22 KB, 1219x794, coins.png [View same] [iqdb] [saucenao] [google] >>12421758 sorry, wrong photo

Anonymous Sat Dec 5 02:11:43 2020 No.12421788

>>12421759
Yes. I see the problem now. With coin flips, there's an inherent ordering. When you're dealing with two doors opened in different ways, the order doesn't matter. This fact is occluded by memes, so anon ends up counting the two different configurations as the same.

>>	Anonymous Sat Dec 5 02:19:08 2020 No.12421807 >>12421758 TOSS THE FUCKING COINS IRL AND FIND OUT

>>	Anonymous Sat Dec 5 02:20:32 2020 No.12421810 >>12421758 HH happens 1/3 of all cases according to your picture

Anonymous Sat Dec 5 02:34:18 2020 No.12421846

>>12421788
well, yeah. if one of two coins is guaranteed heads, then - obviously - only the other coin needs to be flipped, making it a 50% chance. i just included both guaranteed heads scenarios to make it more readable.
scenario 3 can be read in reverse order to be scenario 1 and scenario 4 can be read in reverse to be scenario 2. ultimately which coin is guaranteed heads is arbitrary

Anonymous Sat Dec 5 02:40:23 2020 No.12421861
File: 34 KB, 1024x768, venn for brainlet anons.png [View same] [iqdb] [saucenao] [google]

>>12421759
Problem here is you consider the event HH (both heads) to actually be two separate events where each is part of either set when it's not.
HH is both part of (1st coin is heads) and (2nd coin is heads) in the sense that (1st coin is heads) ∩ (2nd coin is heads) = HH

>>	Anonymous Sat Dec 5 02:43:47 2020 No.12421867 >>12421861 i don't see the issue with that train of thought. whichever coin is guaranteed heads, there is one remaining coin to flip; which has a 50% chance of landing heads. HT, TH and HH are not 3 equally likely scenarios

Anonymous Sat Dec 5 02:52:34 2020 No.12421880

>>12421846
if one of two coins is guaranteed heads, 1/3 of the time you will get both heads, not a 50% chance.
Because one of the two coins is guaranteed heads 3/4 of the time, and both are heads 1/4 of the time.
Given one of two coins is guaranteed heads, both are heads = 1/4 probability INSIDE that 3/4 probability: 1/4 / 3/4 = 1/3.
Sounds counter intuitive but was proven empirically idk how many times.

>>	Anonymous Sat Dec 5 02:57:28 2020 No.12421888 >>12421867 There is no coin guaranteed to ve heads

Anonymous Sat Dec 5 03:02:41 2020 No.12421901

>>12421867
Look at your picture closely.
Your tree is not a representation of outcomes, in the sense that its two branches each represent one arbitrarily chosen event and the specific outcomes that satisfy its condition.
Scenario 2 and 4 are actually one and the same, you are just showing it is a child of each event, which is true, but the number of appearences in this tree doesn't represent the actual probability of outcomes. It's a hierarchy tree composed of selected sets and their child elements, some of which can belong to both at the same time, as shown in >>12421861
If the venn diagramm doesnt do it for you, >>12420422 is actually a very concise way of representing the different outcomes of the total set, each with aprobability of 1/4.

Anonymous Sat Dec 5 03:04:13 2020 No.12421904

>>12421888
>You flip two coins, at least one is HEADS.
???

>>12421880
both of the coins being heads is only a 1/4 chance when no coins have guaranteed outcomes. (1/2*1/2) both coins being tails being eliminated brings up this chance as only one coin is chance dependent,

>>	Anonymous Sat Dec 5 03:05:39 2020 No.12421905 >>12421888 I think anon refers to "at least one is heads", in the sense that events that satisfy this condition are guaranteed to have one coin that is heads. It doesn't refer to a specific coin of course, no actual order here.

Anonymous Sat Dec 5 03:10:03 2020 No.12421914

>>12421904
>both of the coins being heads is only a 1/4 chance when no coins have guaranteed outcomes.
Of course, that is what "1/4 probability INSIDE that 3/4" means.
P( both are heads | at least one is heads ) = P ( both are heads ∩ at least one is heads ) / P( at least one is heads )
= P ( both are heads ) / P( at least one is heads ) = 1/4 / 3/4 = 1/3

Anonymous Sat Dec 5 03:14:32 2020 No.12421926

>>12421901
wouldn't scenarios 2 and 4 being the same bring it back to being 50% chance? i feel like i'm being stubborn here but it just doesn't make sense to me how an outcome determined by one coin flip can be anything other than one half. whether the "second" or "first" coin is the guaranteed head the only factor separating a "both heads" and a "one heads" scenario is one coin flip.

>>	Anonymous Sat Dec 5 03:19:32 2020 No.12421935 https://youtu.be/Ke8TZj63F0Q

>>	Anonymous Sat Dec 5 03:33:37 2020 No.12421962 this thread has the highest proportion of bait ive ever seen. either that or mass hysteria.

Anonymous Sat Dec 5 03:35:47 2020 No.12421965

>>12421926
>i feel like i'm being stubborn here
dont worry it's really not bad compared to what we've seen previously

Nothing tells us the coins are thrown consecutively, so there's no real order here.
However, since the coins are independant, we can use an order for labelling purposes.
The coins are independant.
That means the first coin being heads and the second being tails is NOT the same event as the first one being tails and the second being heads.
HT /= TH.

Looking at >>12420422, you can see the total set is composed of every possible event given 2 coins with 2 stats each : 2^2 = 4, with flat distribution, i.e. equal probability of 1/4.
Notice how the HT/TH comes up twice, that's why we make the distinction between the two events, in relation to the order we label them.
If we consider the condition "at least one is heads", we remove TT.
We are therefore dealing with 3 events. (which previously represented 3/4 of the total set)
Remember, each are distinct events with equal probability. The 3 of them share the total set with a probability of 1/3 each.
HH appears once with a probability of 1/3.

If I want to refer to the 1/4 / 3/4 thing, 4 is the total set, 3 is the events we keep that satisfy at least one is heads and 1 is the HH event. We remove TT and keep 3, only want HH so it's 1 out of 3.

>>	Anonymous Sat Dec 5 03:45:14 2020 No.12421987 >>12421962 all 3 threads make for over 1200+ posts combined lmao

Anonymous Sat Dec 5 03:47:46 2020 No.12421989

>>12421926
Flip two coins. If it's TT, discard the trial, otherwise write down the result. Doesn't matter if you flip consecutively, or simultaneously, doesn't matter if the coins Are labeled or not. Do it until you have 100 trials written down.

"At least one is heads" is true for every pair in your list. But it's clear that the train of thought "1/2 chance first coin is heads, then 1/2 chance other coin is also heads etc." doesn't work here.

Anonymous Sat Dec 5 04:03:40 2020 No.12422023 [DELETED]

File: 72 KB, 220x220, 220.png [View same] [iqdb] [saucenao] [google]

>>12418876
>you flip 2 coins
>at least 1 is heads
You have the event of flipping two coins but then you added a constraint that makes no fucking sense. What if they're both tails? Competely nonsensical proplem. If anything it should say "if you look at one of the coins and it is heads, what is the probability that the other coin is heads" which is a trivial since both coins are presumably independent. The answer is 50%

>>	Anonymous Sat Dec 5 04:06:45 2020 No.12422027 >>12422023 t. doesn't know what conditional probability is

>>	Anonymous Sat Dec 5 04:12:43 2020 No.12422035 >>12422027 Fuck you

>>	Anonymous Sat Dec 5 04:15:54 2020 No.12422042 >>12421965 i get the logic here, but fail to see how both HH scenarios are counted as one but both non-HH scenarios aren't. as the probability of an HH scenario is the main question TH may as well = HT as they are both not HH

>>	Anonymous Sat Dec 5 04:35:50 2020 No.12422099 I flip two coins and one of them is heads. So I have HH, HT, TH. HT is the same event as HT: one heads and one tails. So I have HH, and HT. So its 50/50 between the two: one heads one goals or two heads

>>	Anonymous Sat Dec 5 04:43:06 2020 No.12422113 File: 50 KB, 1218x832, coin diagram.png [View same] [iqdb] [saucenao] [google] this is the conclusion i've come to; fairly sure it's airtight. just depends on how you interpret the question.

Anonymous Sat Dec 5 04:43:34 2020 No.12422116

>>12422099
Hmmmm I am retarded. I was looking at it as if the question is H-, so what is the probability of second coin being heads or tails. If we did 1000 flips, we'd expect 250 HH, 250 HT, 250 TH, 250 TT. We know that TT is out of the question so we reduce our sample space to 250 HH, 250 HT, 250 TH. Know the question asks what is the probability that both are heads. It would 250/750, 1/3.

>>	Anonymous Sat Dec 5 04:50:56 2020 No.12422135 ITT: /sci/ seethes over what the probability of two 50/50 outcomes is. Goddamn.

Anonymous Sat Dec 5 05:08:57 2020 No.12422188

>>12422113
think about scenario 2 that you wrote down. How the fuck is TH going to occur in practice? If you have to guarantee atleast 1 heads then you have to throw any scenario with the first coin being tails out, because that elimates HH. That is not at all how you do "atleast 1 coin is heads" the only scenario that makes sense for the mathematical statement "atleast 1 heads" is scenario 1.

>>	Anonymous Sat Dec 5 05:28:40 2020 No.12422243 >>12422188 i just did that to demonstrate that the number coin that is guaranteed heads doesn't matter. take out that one and it still stands.

>>	Anonymous Sat Dec 5 05:52:31 2020 No.12422307 >>12422135 exactly, except you're wrong.

>>	Anonymous Sat Dec 5 06:06:36 2020 No.12422331 >>12422113 No you fucking mong, while your scenarios are true as seen here >>12419050, there's no two ways to interpret the question, rearanging the coins so that it's always the first one that's head is your own wrong headcanon

>>	Anonymous Sat Dec 5 06:52:37 2020 No.12422434 >>12420955 >Yeah, and? And what? You're the one who asked me.

>>	Anonymous Sat Dec 5 06:53:39 2020 No.12422436 >>12420974 >Is referring to a coin flip in the pair being heads. No, it's referring directly to the first clause of the sentence, not to something else.

>>	Anonymous Sat Dec 5 06:54:40 2020 No.12422441 >>12420979 >"At least one is heads" Refers to two coin flips, which resulted in one or more heads.

>>	Anonymous Sat Dec 5 06:55:41 2020 No.12422445 >>12421004 >So you agree I'm right I agree that the first clause of the sentence is two coin flips, not a single coin. You seem to disagree, but maybe you're not expressing yourself clearly.

Anonymous Sat Dec 5 06:56:42 2020 No.12422447 [DELETED]

>>12421037
>it should be of all coins where a head is observed, how many are part of a pair of heads.
>should be
I do realize you think question "should be" something different. Perhaps something exciting and bold, something which would allow you to favorably showcase your pet wikipedia article.

Alas, it's the same boring question it's always been, about two coin flips with a result of one or more heads.

Anonymous Sat Dec 5 06:59:09 2020 No.12422450 [DELETED]

>>12422445
>>12421037
>it should be of all coins where a head is observed, how many are part of a pair of heads.
>should be
I do realize you think the question "should be" something different. Perhaps something exciting and bold, something which would allow you to favorably showcase your pet wikipedia article.

Alas, it's the same boring question it's always been, about two coin flips with a result of one or more heads.

Anonymous Sat Dec 5 07:00:19 2020 No.12422451

>>12421037
>it should be of all coins where a head is observed, how many are part of a pair of heads.
>should be
I do realize you think the question "should be" something different. Perhaps something exciting and bold, something which would allow you to favorably showcase your pet wikipedia article.

Alas, it's the same boring question it's always been, about two coin flips with a result of one or more heads.

>>	Anonymous Sat Dec 5 07:04:31 2020 No.12422457 It’s 50 %. Incorrectly scripted run-downs doesn’t prove anything. Shit in = shit out.

>>	Anonymous Sat Dec 5 08:06:23 2020 No.12422578 Why someone always have to post an uber shit tier bait thread like that and why the fuck everyone comes to answer and go on a crusade. Why the fuck won't you let these worthless fucking threads die?

>>	Anonymous Sat Dec 5 08:20:01 2020 No.12422618 >>12420164 Obsessed

>>	Anonymous Sat Dec 5 08:36:49 2020 No.12422643 >>12421023 >get two coins, toss both at the same time, record if there are 1 head or 2. You already know one coin is heads, you just need to flip one coin.

>>	Anonymous Sat Dec 5 08:39:18 2020 No.12422645 >>12421709 >"At least one is heads" refers to a number of coins among two that is not zero. {1, 2} This doesn't contradict anything I said. Only one coin is known to be heads.

>>	Anonymous Sat Dec 5 08:40:56 2020 No.12422648 >>12421720 I did consider both cases. >>12421734 No, you said we are dealing with coordinates in R.

>>	Anonymous Sat Dec 5 08:41:58 2020 No.12422649 >>12421758 Yes.

Anonymous Sat Dec 5 08:43:10 2020 No.12422651

>>12422643
>You already know one coin is heads,
No, all you know is that there are two coin flips, which resulted in one or more heads.
>you just need to flip one coin.
No, you already flipped two coins. You don't flip one of those two coins again later.

>>	Anonymous Sat Dec 5 08:44:48 2020 No.12422655 >>12422434 And how does that contradict anything I said?

>>	Anonymous Sat Dec 5 08:46:48 2020 No.12422660 >>12422655 How does what contradict what?

>>	Anonymous Sat Dec 5 08:47:00 2020 No.12422662 >>12422436 >No, it's referring directly to the first clause of the sentence, not to something else. Yeah, I never said anything to the contrary. Obviously one coin in the pair being heads refers to the pair and not some other coins.

>>	Anonymous Sat Dec 5 08:48:42 2020 No.12422667 >>12422441 Right, it refers to a coin in the pair being heads. >I agree that the first clause of the sentence is two coin flips, not a single coin. OK, and what is your point? >You seem to disagree Where?

>>	Anonymous Sat Dec 5 08:50:14 2020 No.12422670 >>12422667 >>12422662 There is no reference to a single coin, only to the result of two coin flips.

>>	Anonymous Sat Dec 5 08:50:25 2020 No.12422671 >>12422451 >I do realize you think the question "should be" something different. No, your method of representing the question should be different.

>>	Anonymous Sat Dec 5 08:51:32 2020 No.12422673 >>12422671 My method of representing the question is the question itself.

Anonymous Sat Dec 5 08:54:16 2020 No.12422676

>>12422651
>No, all you know is that there are two coin flips, which resulted in one or more heads.
That doesn't disagree with anything I said.

>No, you already flipped two coins. You don't flip one of those two coins again later.
Flipping two coins and then looking at the result is not following the question. You don't get to look at the coins, you are only told one is heads. Therefore the only way of modeling the question is to stemming the probability the other coin is heads. This is done by flipping one coin.

>>	Anonymous Sat Dec 5 08:55:18 2020 No.12422678 >>12422660 How do your posts contradict my posts? I never said the second sentence is talking about other coins.

>>	Anonymous Sat Dec 5 08:56:21 2020 No.12422679 >>12422670 >There is no reference to a single coin "At least one is heads"

>>	Anonymous Sat Dec 5 08:57:23 2020 No.12422680 >>12422673 Where in the question do you get to determine the results of both coins? You are only told one is heads.

>>	Anonymous Sat Dec 5 08:58:56 2020 No.12422683 >>12422679 >"At least one is heads" This refers directly to the first clause of the sentence: "You flip two coins."

>>	Anonymous Sat Dec 5 08:59:58 2020 No.12422687 >>12422680 The result of both coins is one or more heads.

>>	Anonymous Sat Dec 5 09:01:08 2020 No.12422690 >>12422678 >I never said the second sentence is talking about other coins. I never said you did.

>>	Anonymous Sat Dec 5 09:01:37 2020 No.12422691 >>12422683 >This refers directly to the first clause of the sentence: "You flip two coins." Right, I never said it referred to some other coins. What is your point?

>>	Anonymous Sat Dec 5 09:03:00 2020 No.12422693 >>12422687 Where in the question do you get to determine the results of both coins? You are only told one is heads. >>12422690 Then why are you repeatedly telling me it refers to the first sentence?

>>	Anonymous Sat Dec 5 09:04:52 2020 No.12422699 >you are only told one is heads No, you are told that you flip two coins, which resulted in one or more heads. That all you're told. Nothing more, nothing less.

>>	Anonymous Sat Dec 5 09:06:42 2020 No.12422703 >>12422693 >Where in the question do you get to determine the results of both coins? The part where it says "You flip two coins, at least one is heads." >You are only told one is heads. No, you are told that two coin flips results in one or more heads.

>>	Anonymous Sat Dec 5 09:07:45 2020 No.12422709 >>12422691 >What is your point? That's what I'm asking you.

>>	Anonymous Sat Dec 5 09:08:23 2020 No.12422712 >>12422699 >which resulted in one or more heads. Actually you're told "at least one is heads" which implies one or more heads. I don't know why you keep repeating non sequitur as responses.

>>	Anonymous Sat Dec 5 09:09:33 2020 No.12422716 >>12422703 >The part where it says "You flip two coins, at least one is heads." That's only information about one coin. Saying it determines both coins is fake information.

>>	Anonymous Sat Dec 5 09:10:16 2020 No.12422717 >>12422693 >Then why are you repeatedly telling me it refers to the first sentence? I'm not sure what your question is here? The second clause of the first sentence refers to the first clause of the first sentence.

>>	Anonymous Sat Dec 5 09:10:35 2020 No.12422719 >>12422709 No, you didn't ask that. You responded to my posts with non sequitur. Read my posts again if you don't get it.

>>	Anonymous Sat Dec 5 09:12:20 2020 No.12422724 >>12422717 >I'm not sure what your question is here? Why are you repeatedly telling me the second clause of the first sentence refers to the first clause of the first sentence? I never said it doesn't.

Anonymous Sat Dec 5 09:13:07 2020 No.12422726

>>12422712
>which implies one or more heads
Correct, one or more of two coin flips resulted in heads.
>>12422716
>That's only information about one coin
No, it's information about the result of two coin flips. The second clause refers directly to the first, not to something else.

>>	Anonymous Sat Dec 5 09:15:49 2020 No.12422734 >>12422724 >I never said it doesn't. Yes, you keep saying the second clause of the sentence refers to a single coin, when it clearly refers to the first clause: "You flip two coins."

>>	Anonymous Sat Dec 5 09:17:28 2020 No.12422739 >>12422726 >No, it's information about the result of two coin flips. One coin in the pair being heads is information about the two coin flips. I'm not going to respond to any more of these non sequiturs. Either give an argument or leave.

>>	Anonymous Sat Dec 5 09:18:05 2020 No.12422740 >>12422719 No, your posts say that the second clause of the sentence refers to a single coin, but the only referent is two coin flips.

>>	Anonymous Sat Dec 5 09:18:30 2020 No.12422741 >>12422734 The single coin is one of the two coins. You're not actually making an argument.

>>	Anonymous Sat Dec 5 09:19:06 2020 No.12422743 >>12422739 >One coin in the pair being heads is information about the two coin flips. It would be, if we were given that information, but we weren't.

>>	Anonymous Sat Dec 5 09:20:07 2020 No.12422746 >>12422741 Which single coin? No single coin is ever referred to. The only reference is to the result of two coin flips.

>>	Anonymous Sat Dec 5 09:24:46 2020 No.12422766 >>12422743 We were given that information, it's just not information that determines the result of both coins, only one.

>>	Anonymous Sat Dec 5 09:26:03 2020 No.12422769 >>12422746 >Which single coin? Whichever one is referred to as "one is heads." It didn't matter which one, since the probability is the same either way.

>>	Anonymous Sat Dec 5 09:27:05 2020 No.12422773 >>12422766 There is never a reference to any single coin, only to the result of two coin flips.

>>	Anonymous Sat Dec 5 09:28:08 2020 No.12422775 >>12422769 >Whichever one is referred to as "one is heads." No single coin is ever referred to as being heads.

>>	Anonymous Sat Dec 5 09:28:14 2020 No.12422777 >>12422773 >There is never a reference to any single coin "At least one is heads"

>>	Anonymous Sat Dec 5 09:29:03 2020 No.12422780 >>12422769 >Saying "one is heads" increases the chance of both coins being heads.

>>	Anonymous Sat Dec 5 09:29:16 2020 No.12422782 >>12422775 See >>12422777

>>	Anonymous Sat Dec 5 09:31:18 2020 No.12422789 >>12422777 >>12422782 That's a reference to the first clause of the sentence, "You flip two coins," not to anything else.

>>	Anonymous Sat Dec 5 09:31:36 2020 No.12422790 >>12422780 Saying one is heads increases the chance of one coin in the pair being heads to 1, yes. The other remains 1/2 since the coins are independent.

>>	Anonymous Sat Dec 5 09:33:19 2020 No.12422795 >>12422789 See >>12422739

>>	Anonymous Sat Dec 5 09:35:24 2020 No.12422807 >>12422795 See >>12422789

>>	Anonymous Sat Dec 5 09:35:42 2020 No.12422808 >>12422807 See >>12422795

>>	Anonymous Sat Dec 5 09:36:26 2020 No.12422810 >>12422808 See >>12422807

>>	Anonymous Sat Dec 5 09:37:34 2020 No.12422815 >>12422810 See >>12422808

>>	Anonymous Sat Dec 5 09:37:36 2020 No.12422816 >>12422790 >Saying one is heads See >>12422789

>>	Anonymous Sat Dec 5 09:38:37 2020 No.12422820 >>12422815 See >>12422810

Anonymous Sat Dec 5 09:38:44 2020 No.12422821
File: 234 KB, 1161x937, countif.jpg [View same] [iqdb] [saucenao] [google]

>>12418876
>>12418962
can someone smarter than me answer this question?
I did a simple excel demo. (yes I could have done it in less steps).
I sum up the iterations with at least one head and put them over the ones with two heads, and as you expect it is about 1/3, .3464 in red here.
What I don't get is why two heads over not two heads is also almost 1/3 (but not the same 1/3 using the same random numbers.) Shouldn't that be 1/4 because it is counting the tt? .360544 here bolded in red.
[its not very close to 1/3 because I only did 200 trials]

>>	Anonymous Sat Dec 5 09:38:49 2020 No.12422822 >>12422816 See >>12422780

>>	Anonymous Sat Dec 5 09:40:31 2020 No.12422825 >>12422822 See >>12422816

>>	Anonymous Sat Dec 5 09:44:35 2020 No.12422834 >>12422821 1/4 : 3/4 = 1 : 3

>>	Anonymous Sat Dec 5 09:49:48 2020 No.12422844 OP is right. It’s 1/2. HH is twice as likely as HT if at least one coin is heads!

Anonymous Sat Dec 5 09:52:33 2020 No.12422852
File: 109 KB, 1353x592, AC3D1032-304C-49AF-A4BB-C800428B7256.jpg [View same] [iqdb] [saucenao] [google]

>>12422834
But then all you need to know is the probability of two heads to get the 1/3 answer for the op,
But that doesn’t make any sense. Knowing that at least one is heads should increase the odds that both are heads, but the odds are about the same, which suggest knowing one is heads is useless, which doesn’t make any sense

>>	Anonymous Sat Dec 5 09:53:26 2020 No.12422855 >>12422844 >if at least one coin is heads No, if a single coin is heads. The question never refers to a single coin, only to the result of two coin flips.

>>	Anonymous Sat Dec 5 10:02:01 2020 No.12422884 >>12422855 I mean as likely. HH is as likely as HT and so the correct answer is 1/2. Any stupid moron can understand this.

>>	Anonymous Sat Dec 5 10:03:53 2020 No.12422893 >>12422852 That’s a big cock when you consider the size of the rest of the body.

Anonymous Sat Dec 5 10:09:15 2020 No.12422903

>>12422852
You flip two coins.
(This is the sample space given by the first clause of the sentence.)
HH HT TH TT = 1/4 : 1/4 : 1/4 : 1/4
HH = 1/4 : 4/4 = 1/4

The result of those two coin flips contains at least one heads.
(This is the additional information given by the second clause of the sentence.)
HH HT TH = 1/4 : 1/4 : 1/4
HH = 1/4 : 3/4 = 1/3

The result of those two coin flips contains one distinct coin we know to be heads and one distinct coin we don't know.
(This information doesn't exist.)
HH HT = 1/4 : 1/4
HH = 1/4 : 2/4 = 1/2
or alternatively
Hh Ht hH tH = 1/4 : 1/4 : 1/4 : 1/4
HH = 2/4 : 2/4 = 1/2

>>	Anonymous Sat Dec 5 10:15:59 2020 No.12422918 >>12422903 you mean >HH = 2/4 : 4/4 = 1/2

>>	Anonymous Sat Dec 5 10:17:42 2020 No.12422923 >>12422918 The last line, yes.

>>	Anonymous Sat Dec 5 10:18:11 2020 No.12422925 >>12422903 That doesn’t answer why 2 heads over not two heads =1/3 even when counting two tails.

>>	Anonymous Sat Dec 5 10:20:16 2020 No.12422932 >>12422884 Flip two coins. Probability of two heads is 1/4 Probability of a heads and a tails is 1/2 Probability of two tails is 1/4. The first two cases contain at least one heads. >HH is as likely as HT 1/4=1/2. >Any stupid moron can understand this.

>>	Anonymous Sat Dec 5 10:22:30 2020 No.12422936 >>12422925 Because you're dividing 1/4 by 3/4, rather than by 1.

>>	Anonymous Sat Dec 5 10:23:08 2020 No.12422938 "flip 2 coins" is meaningless if the result of one of the flips is pre-determined, so that phrase means "flip one coin", so the question reads: "flip one coin, what's the chance it will land on heads?" hint: it's not 1/3

>>	Anonymous Sat Dec 5 10:24:13 2020 No.12422940 >>12419385 Nice code

>>	Anonymous Sat Dec 5 10:25:23 2020 No.12422943 >>12422938 >if the result of one of the flips is pre-determined This information doesn't exist.

>>	Anonymous Sat Dec 5 10:26:56 2020 No.12422944 >>12422938 It is not pre-determined. Regard it as a game, in which two tails constitutes a reflip.

>>	Anonymous Sat Dec 5 10:27:24 2020 No.12422946 >>12422943 >at least one is heads

>>	Anonymous Sat Dec 5 10:28:47 2020 No.12422954 >>12422946 Refers to two coin flips, which resulted in one or more heads.

Anonymous Sat Dec 5 10:30:19 2020 No.12422958
File: 783 KB, 1280x1589, F4EAA60F-5D45-4766-ACE0-E7967057E508.png [View same] [iqdb] [saucenao] [google]

>>12422936
Yes. Is it just a coincidence it’s the right answer? I am only using hh to get the 1/3 answer in the second forulma. I do not need to know one is heads and I still get 1/3. Becuase ai am counting tt as well

Anonymous Sat Dec 5 10:36:17 2020 No.12422985

>>12422958
No, what you're doing is dividing HH by HT TH TT, instead of dividing HH by HH HT TH TT.

One of your calculations is correct: HH by HH TH HT to get 1/3.
The other leaves out HH in the sample space, which is why it's giving you an incorrect answer.

>>	Anonymous Sat Dec 5 10:44:39 2020 No.12423015 >>12422954 >>12422944 the complete roll space is heads-tails/heads-heads, which means we can omit the first heads and we just end up with tails/heads

Anonymous Sat Dec 5 10:46:19 2020 No.12423020

>>12422903
>HH HT TH = 1/4 : 1/4 : 1/4
>HH = 1/4 : 3/4 = 1/3
This is the correct answer, not sure why you kept going
>HH HT = 1/4 : 1/4
Here, you’re not including TH as a possibility as well - if you wanted to combine HT and TH into one it would be
HH HT/TH = 1/4 : 1/2

>>	Anonymous Sat Dec 5 10:47:21 2020 No.12423023 >>12423015 No, the space is HH HT TH TT.

>>	Anonymous Sat Dec 5 10:47:38 2020 No.12423025 >>12423015 It doesn’t specify the 1st flip is the Heads flip, so tails-heads is just as likely as heads-tails (or heads-heads)

>>	Anonymous Sat Dec 5 10:51:10 2020 No.12423045 >>12423020 >not sure why you kept going The third section: >>12422903 >(This information doesn't exist.) explains what extra information you'd need for the answer to be 1/2.

>>	Anonymous Sat Dec 5 10:51:57 2020 No.12423046 >>12423015 If you want to think about it like that, sure. But we have then [math] HH \mapsto \frac13 [/math] and [math] HT\mapsto \frac23 [/math] following from facts we already know about coin flips.

>>	Anonymous Sat Dec 5 10:53:35 2020 No.12423055 >>12423045 So your answer is 1/3? Apologies I misunderstood what your comment was saying

>>	Anonymous Sat Dec 5 10:55:14 2020 No.12423063 >>12423055 Yes, I agree with you that the answer to OP is unambiguously 1/3.

Anonymous Sat Dec 5 11:00:33 2020 No.12423080

>>12418876
I can never be fucked on all the variations, but this problem is part of a family that, if you're struggling with them, all have one secret to understanding the right answer.
>You need to select one thing to be your choices, and another to be your probabilities. Invert your problem setup, plug in the probabilities, and watch the orthodox answer appear.

Anonymous Sat Dec 5 12:21:12 2020 No.12423308

THERE IS NO CONCRETE ANSWER
if you consider coin 1:heads+coin 2:tails and coin1:tails+coin 2:heads as scenarios that are necessarily different (i.e. coins being indexed)
then it's 1/3
if you consider them as effectively same scenarios, it's 1/2.
FUCK OFF WITH THESE MEME THREADS

Anonymous Sat Dec 5 12:31:05 2020 No.12423336

>>12422042
>TH may as well = HT as they are both not HH
it's not just that they aren't HH.
Maybe instead of thinking about order think of it as flipping one coin in each hand (again, just for labeling purposes).
HT: Left hand coin is heads, right hand coin is tails
TH: Left hand coin is tails, right hand coin is heads
Two different events, each have a probability of 1/4.
HH: Both hands have coins. No two separate scenarios to this. Probability of 1/4.
Table on >>12420422 has all the information.
Also proven empirically on >>12419385 , look at the results down.
TT comes up 25% of the time, the combination of HT/TH comes up 50% of the time (1/4 + 1/4) and HH comes up 25% of the time.

>>	Anonymous Sat Dec 5 12:33:03 2020 No.12423340 >>12422116 very good on correcting yourself there anon

>>	Anonymous Sat Dec 5 12:36:57 2020 No.12423353 >>12422645 >This doesn't contradict anything I said. It does. Because this shit: >Only one coin is known to be heads. You have {1, 2} and are only considering the {1}

>>	Anonymous Sat Dec 5 12:38:57 2020 No.12423356 >>12422648 >No, you said we are dealing with coordinates in R. I never said such thing schizo >OMG ITS YOU!!!! YOU'RE ANONYMOUS!!!!! >I did consider both cases. But you didn't: >Only one coin is known to be heads.

>>	Anonymous Sat Dec 5 12:42:47 2020 No.12423365 >>12422740 this. he's so retarded

>>	Anonymous Sat Dec 5 12:44:49 2020 No.12423371 >>12422769 >>12422777 That statement can be made by seeing both coins and seeing they are both heads, which satisfies "at least one is heads"

>>	Anonymous Sat Dec 5 12:51:33 2020 No.12423386 >>12423308 >same scenarios thing is they are not as shown empirically. So first answer is the right answer

>>	Anonymous Sat Dec 5 12:52:33 2020 No.12423390 >>12423308 >THERE IS NO CONCRETE ANSWER 1/3 is the only answer that matches the information given in the question. >if you consider them as effectively same scenarios No information is given that would allow you to do that.

Anonymous Sat Dec 5 13:00:22 2020 No.12423411

>>12423390
>No information is given that would allow you to do that.
and no information given doesn't allow it, that's why this meme is shit. it's up to interpretation as some people would consider 2/3 possible scenarios as effectively the same scenario.
should you not eliminate scenarios that are only different by technicalities that are not important?

>>	Anonymous Sat Dec 5 13:05:35 2020 No.12423429 >>12423411 >no information given doesn't allow it You have to add information in order to allow it.

>>	Anonymous Sat Dec 5 13:06:15 2020 No.12423432 >>12423429 and you have to add information to index the coins

>>	Anonymous Sat Dec 5 13:09:48 2020 No.12423448 >>12423432 The first clause of the first sentence gives you that information. "You flip two coins" exactly and unambiguously gives you a sample space of HH HT TH TT.

Anonymous Sat Dec 5 13:12:14 2020 No.12423457

"You flip two coins"
>consider the sample space {HH, TH, HT, TT} with uniform distribution P
"At least one is heads"
>define new distribution P'(A)= P(A|not TT)
"What's the probability that both are heads?"
>compute P'(HH)

it's not possible to pass an undergrad course in probability and see something different

>>	Anonymous Sat Dec 5 13:14:30 2020 No.12423464 >>12423411 no constraints => total sample space constraints => total sample space - values removed by constraints no information given about a certain characteristic of the set => no constraints on this characteristic

>>	Anonymous Sat Dec 5 14:27:35 2020 No.12423723 This is a textbook problem. The answer is 1/2

>>	Anonymous Sat Dec 5 16:48:26 2020 No.12424159 100%

>>	Anonymous Sat Dec 5 17:57:40 2020 No.12424406 File: 64 KB, 709x657, american coin.png [View same] [iqdb] [saucenao] [google]

>>	Anonymous Sat Dec 5 18:09:01 2020 No.12424434 >>12424406 Too much data to process without a denomination and date range. Perhaps RenTech could help.

>>	Anonymous Sat Dec 5 18:55:09 2020 No.12424616 >>12423723 explain the 1/2 answer i don’t get it

>>	Anonymous Sat Dec 5 18:56:01 2020 No.12424621 File: 378 KB, 2440x2164, coins.png [View same] [iqdb] [saucenao] [google] >only assuming 1 dimension did you guys drop out of elementary school?

>>	Anonymous Sat Dec 5 19:00:31 2020 No.12424646 >>12420422 >each square has an equal chance (25%) of occurring. HH has double the chance See >>12419486

>>	Anonymous Sat Dec 5 19:02:45 2020 No.12424661 >>12424646 1/2+1/2+1/4>1, dummy

>>	Anonymous Sat Dec 5 19:07:48 2020 No.12424677 This thread tells me everything I need to know about /sci/. Thanks. Saved me a lot of time.

Anonymous Sat Dec 5 19:09:54 2020 No.12424688

>>12418876
You don't need to label the coins to get the right answer (1/3) because the 3 scenarios aren't all equally likely: #2 happens 1/2 of the time, and #1 and #3 happen 1/4 of the time. The probability of at least one coin being heads is #2+#3=1/2+1/4=3/4, and the probability of both is #3=1/4, so the answer is (1/4)/(3/4)=1/3.

>>	Anonymous Sat Dec 5 19:10:13 2020 No.12424689 >>12424677 This is the adult pool, have fun swimming in toddler piss.

>>	Anonymous Sat Dec 5 19:11:24 2020 No.12424692 >>12424646 >HH has double the chance Of what?

>>	Anonymous Sat Dec 5 19:22:58 2020 No.12424727 File: 30 KB, 450x123, 58D83F5D-F2D0-4F22-A2EB-E84D1CFEBC53.jpg [View same] [iqdb] [saucenao] [google] What did the R meister mean by this? Did he literally dilate?

>>	Anonymous Sat Dec 5 19:29:26 2020 No.12424749 >>12424727 lazy caterer checked

Anonymous Sat Dec 5 19:36:16 2020 No.12424776

There's no way there's this many low IQ mongrels ITT. Let me break down the possibilities.

If the left coin is the guaranteed heads:
HH
HT
If the right coin is the guaranteed heads
HH
TH
This brings the possibilities to:
HH
HH
HT
TH
Two of them are both heads out of the four combinations.
2/4 is 1/2.

>>	Anonymous Sat Dec 5 19:36:59 2020 No.12424781 >>12422643 That is not what "at least one coin is heads" means.

>>	Anonymous Sat Dec 5 19:37:27 2020 No.12424784 >>12424776 >If the left coin is the guaranteed heads: >If the right coin is the guaranteed heads not how it works, anon

>>	Anonymous Sat Dec 5 19:51:26 2020 No.12424829 >>12424784 >>12424781 Actual retard.

Anonymous Sat Dec 5 19:55:00 2020 No.12424839

the confusion arrises from the fact that people what people perceive as "atleast one heads" is actually a STRICT SUBSET of "atleast one heads" and not an equality.

>I flip a coin and it is heads so atleast one is heads

yes that is a subset but not all of the scenarios that "atleast one heads" entails

>If the left coin is the guaranteed heads: If the right coin is the guaranteed heads

again a subset but not an equality.

>>	Anonymous Sat Dec 5 19:55:09 2020 No.12424841 >>12424829 see >>12419385

Anonymous Sat Dec 5 19:56:10 2020 No.12424846

>>12424776
>Flip two coins:
>25% chance of both heads, 50% chance of one heads and one tails, 25% chance of both tails
>Flip two coins and announce whether a heads showed up
>Suddenly, 50% chance of both heads, 50% chance of a heads and a tails, 25% chance of both tails.
Amazing.

>>	Anonymous Sat Dec 5 22:13:59 2020 No.12425244 >>12422855 >No, if a single coin is heads. A single coin is heads of at least one is heads, moron.

>>	Anonymous Sat Dec 5 22:16:09 2020 No.12425251 >>12423353 >>Only one coin is known to be heads. >You have {1, 2} and are only considering the {1} Not sure what you're talking about, you think the second coin is heads too?

>>	Anonymous Sat Dec 5 22:17:35 2020 No.12425254 >>12423356 >I never said such thing schizo Then read the posts you're responding to retard. >But you didn't: >>Only one coin is known to be heads. I did. Only one coin is known to be heads.

>>	Anonymous Sat Dec 5 22:19:03 2020 No.12425259 >>12422740 >No, your posts say that the second clause of the sentence refers to a single coin It does. "At least one is heads." >but the only referent is two coin flips. The two flips contain the single heads.

>>	Anonymous Sat Dec 5 22:20:39 2020 No.12425264 >>12423371 >That statement can be made by seeing both coins Who saw both coins? You're making up fake information not in the problem.

>>	Anonymous Sat Dec 5 22:25:15 2020 No.12425272 >>12423448 "at least one is heads" unambiguously tells you that the sample space is Hh hH Ht tH

>>	Anonymous Sat Dec 5 22:27:26 2020 No.12425276 >>12424692 HT or TH

>>	Anonymous Sat Dec 5 22:28:28 2020 No.12425279 >>12424781 It is. If you think anything else you are a schizo.

Anonymous Sat Dec 5 22:32:09 2020 No.12425284

>>12424846
>>Flip two coins and announce whether a heads showed up
Actually it just says "at least one is heads"

>>Suddenly, 50% chance of both heads, 50% chance of a heads and a tails, 25% chance of both tails.
No, there's a 0% chance of both tails, you goddam retard. The chance of two heads is increased because two heads makes it twice as likely a heads is given.

>>	Anonymous Sat Dec 5 22:33:48 2020 No.12425289 >>12424839 There is no confusion, just a schizo who thinks his interpretation is the only one possible getting trolled by people who know it's an ambiguous problem.

Anonymous Sat Dec 5 22:46:11 2020 No.12425317

>>12425251
>Not sure what you're talking about, you think the second coin is heads too?
I'm talking about this :
X being the number of known coins.
"At least one is heads" sets a lower limit. (X ≥ 1)
Two coins sets the upper limit. (X ≤ 2)
X ≤ 2 ∩ X ≥ 1 = (X = 1) ∪ (X = 2)
Two coins. "At least one is heads" can be concluded by seeing either one coin being heads, OR seeing both coins to find that both are heads or one is heads and the other is tails.
OR as in union. You need to consider all values in the resulting set.

>>12425254
>I did. Only one coin is known to be heads.
That is (X=1). You didn't consider (X=2). That is what I am trying to tell you.

>>12425264
>Who saw both coins? You're making up fake information not in the problem.
Not fake information. (X=2) is still in the resulting set. Inventing a constraint that removes it is fake information.

>>	Anonymous Sat Dec 5 22:50:16 2020 No.12425325 >>12418876 I gave a concise explanation of this problem in the last thread and no one listened to me so fuck off

>>	Anonymous Sat Dec 5 22:59:54 2020 No.12425351 >>12425325 what was your answer?

>>	Anonymous Sat Dec 5 23:12:16 2020 No.12425374 50%. The second flip has nothing to do with the result of the first flip

>>	Anonymous Sat Dec 5 23:14:26 2020 No.12425381 50% of anons don't know basic conditional probability

>>	Anonymous Sun Dec 6 01:38:09 2020 No.12425709 S

>>	Anonymous Sun Dec 6 01:39:18 2020 No.12425713 C

>>	Anonymous Sun Dec 6 01:40:20 2020 No.12425715 I

>>	Anonymous Sun Dec 6 01:41:23 2020 No.12425720 no no no

>>	Anonymous Sun Dec 6 01:42:33 2020 No.12425723 S

>>	Anonymous Sun Dec 6 01:43:58 2020 No.12425726 C

>>	Anonymous Sun Dec 6 01:44:22 2020 No.12425729 H

>>	Anonymous Sun Dec 6 01:45:18 2020 No.12425730 I

>>	Anonymous Sun Dec 6 01:45:40 2020 No.12425733 Z

>>	Anonymous Sun Dec 6 01:46:23 2020 No.12425735 O

>>	Anonymous Sun Dec 6 01:47:07 2020 No.12425737 T

>>	Anonymous Sun Dec 6 01:47:27 2020 No.12425739 H

>>	Anonymous Sun Dec 6 01:48:11 2020 No.12425744 R

>>	Anonymous Sun Dec 6 01:48:34 2020 No.12425745 E

>>	Anonymous Sun Dec 6 01:49:23 2020 No.12425746 A

>>	Anonymous Sun Dec 6 01:49:47 2020 No.12425750 D

Anonymous Sun Dec 6 04:48:34 2020 No.12426099

[math]X[/math] - number of heads on both coins
[eqn]P(X = x) = \begin{cases} \frac{1}{4}, & x = 0 \\
\frac{1}{2}, & x = 1\\
\frac{1}{4}, & x = 2 \\
0 & \text{otherwise}
\end{cases}[/eqn]

at least one is heads - [math]P(X \geq 1) = P(X = 1) + P(X = 2) = \frac{3}{4}[/math]

both are heads - [math]P(X = 2) = \frac{1}{4}[/math]

both are heads with the constraint that at least one is heads - [math]P(X = 2 | X \geq 1) = \frac{P(X = 2)}{P(X \geq 1)} = \frac{\frac{1}{4}}{\frac{3}{4}} = \frac{1}{3}[/math]

>>	Anonymous Sun Dec 6 05:18:15 2020 No.12426139 The results is Theyre already both heads and tails

>>	Anonymous Sun Dec 6 08:09:06 2020 No.12426460 >>12425276 where does it say the coin is biased?

Anonymous Sun Dec 6 08:54:42 2020 No.12426515

>>12425317
>X being the number of known coins.
>"At least one is heads" sets a lower limit. (X ≥ 1)
No, it doesn't say at least one is known, it says at least one is heads. If you can assume both are known why not just assume both are heads?

>You didn't consider (X=2).
I didn't add fake info to the problem.

>(X=2) is still in the resulting set.
Resulting set of what?

>>	Anonymous Sun Dec 6 09:00:47 2020 No.12426521 >>12426099 HH HT TH TT Half of the coins are heads so P(at least one is heads) = 1/2 P(both heads\|at least one is heads) = (1/4)(1)/(1/2) = 1/2

>>	Anonymous Sun Dec 6 09:01:49 2020 No.12426525 >>12426460 Where did I say it was?

>>	Anonymous Sun Dec 6 09:22:39 2020 No.12426560 >>12425244 >A single coin is heads of at least one is heads This would be true if there were at most one coin flip, but the first clause of the first sentence tells us there are two coin flips.

>>	Anonymous Sun Dec 6 09:23:36 2020 No.12426563 >>12426560 >This would be true if there were at most one coin flip No, it's true either way. One coin is one coin regardless of other coins.

Anonymous Sun Dec 6 09:23:42 2020 No.12426564

>>12425259
>It does. "At least one is heads."
No, that refers to the result of two coin flips, not to a single coin.
>The two flips contain the single heads.
There is no single heads. The two flips result in one or more heads, not in a single coin that is heads.

>>	Anonymous Sun Dec 6 09:24:43 2020 No.12426566 >>12425272 No, it reduces the sample space established by the first clause of the first sentence from HH HT TH TT to HH HT TH. See >>12422903

Anonymous Sun Dec 6 09:25:45 2020 No.12426568

>>12425289
>who know it's an ambiguous problem
Ambiguous means that something is open to more than one interpretation. OP is the opposite of that. Adding information that doesn't exist, information about a single coin, doesn't describe a different interpretation of the same question. It describes a different question.

>>	Anonymous Sun Dec 6 09:31:59 2020 No.12426575 >>12426563 >No, it's true either way. No, if there are two or more flips that result in one or more heads, no information has been given about any single coin.

>>	Anonymous Sun Dec 6 09:46:25 2020 No.12426609 >>12426525 if HH is twice as likely as HT or TH that means P(H)=2/3, P(T)=1/3 why is the coin funny?

>>	Anonymous Sun Dec 6 10:22:15 2020 No.12426708 >>12426521 >Half of the coins are heads so P(at least one is heads) = 1/2 3 out of 4 cases satisfy "at least one is heads"

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/sci/ - Science & Math