/sci/ - Science & Math

P(H2lH1)= 0.5

Given that a coin came up heads, what's the probability that the next coin flip will come up heads?

50%.

The wording of the question is designed to deceive. It starts with two coin flips, leading some to want to consider the probability of getting two heads from two coin flips. However, the problem quickly narrows itself down to a single flip.

>>2039001
/thread

50% because either the second one is head or then it isn't.

Probability is based on future events. If you know one is heads, the probability of it being heads is 1. Therefore, the only unset variable is the second coin which has a .5 probability of being heads. Therefore, the overall probability of both being heads is .5.

Basically, you might as well only flip one coin if you know for certain one of them is heads.

36pi

lok, jk, its 1/3

Didn't we discuss this before with like 280 posts just a few days ago with that exact same picture. Must be seeing things.

The final system has four possible outcomes:
heads/heads
heads/tails
tails/heads
tails/tails

If one of the coins has landed heads, that rules out one of the finals outcomes, leavings heads/heads, heads/tails, and tails/heads. One of these three outcomes has two coins coming up heads, so there's a 33% possibility that the other coin is heads.

So 33%

>>2039006
>>2039005
>>2039003
>>2039001
TROLLTROLLTROLLTROLLTROLL

The question is ambiguous, both 50% and 1/3 can be considered correct. Read the following link why:
http://en.wikipedia.org/wiki/Boy_or_Girl_paradox

>>2039009
>>2039001
See, these are the two results /a/ is having a fit about

Just one thing:
It doesn't say the FIRST one is heads, it says AT LEAST ONE is heads.

if you know which one is head, and you flip the second (same thing as only flipping one) its 50%

if either one is head, its 33%

tl;dr bad wording to make faggots rage

1/3, also /a/ is smarter than /sci/.

>>2039021

Do it yourself. Use your brain, see this post:
>>2039015
And see what makes sense.

You guys are faggots, both coins must come up heads.
The "At least one is heads" is completely irrelevant, even if one flips tails, you lose.

dohoho

This was going pretty well last night

>>2039020
You, good sir, have just won the internets...or at least this discussion.

at least one is heads.


Sample Space: {HH, HT, TH}

Event: {HH}

Probablity is 1/3.

>>2039015
No, tails/tails/ isn't possible and heads/tails, tails/heads are equivalent the way the the question is worded. Order doesn't matter. It's a combination, not a permutation.

.5

>>2039030
But we already know that one of them is heads, so we only need to know the result of the second, meaning we have a 50% chance

this is the board for dawkinheads and science fanboys, not anyone who knows shit.

>>2039041
a fair coin is flipped twice. If it landed heads at least once, what is the probability that it landed heads twice?

>>2039055
Don't forget the trolls!

Trick question. They're both double-headed coins.

>>2039041
In that case, the possibilities would be:
25% Both heads
25% Both tails
50% One of each

So the statistics would be the same.

>>2039058
That's not the question though, one of the events is already set.

The question states, "At least one is heads". That means that one of the probabilities, either one but not both, is P(H)=1. Since order doesn't matter, we have either:

1*0.5=0.5
or
0.5*1=0.5

You don't even need to flip both coins since we know for certain that the outcome of one of them is heads.

Hey everyone, how about this:

I flip 3,000 coins, at least 2,999 are heads, what is the chance that all 3,000 are heads?

None of the math pointing to 1/3 is correct. You only have one event that matters, as you already know the outcome of 2,999 out of 3,000 flips. P=0.5

>>2039041
>>2039066

Learn to conditional probability faggots.

>>2039034

When doing statistics, that isn't irrelevent. It is called conditional probability. Finding the probability of something happening given something else is already known.

>>2039066
NO.
One of the coin tosses is not 50:50.
The way the question is worded, one of the coins tosses is 1:0.
The statistics are NOT the same.

what's the probability is wont even hit the ground?

>>2039068
You ignored my question.

justasplanned.jpg

>>2039066
Except we already know one is heads. RTFQ

>>2039015
>>2039029
>>2039040

Act. Science major here. These guys are right. The answer is 1/3

>>2039090
>>2039020
>>2039020
>>2039020
I wish I'd have read this post earlier.
I'm done arguing now.

>>2039075
I just flipped two coins. At least one of them is heads. What is the probability that they are both heads?

>>2039098
I just flipped two coins. (again.) at least one is heads. What is the probability that both are heads?

I flip two fair coins, I did not flip two tails. What's the probability that I flipped two heads?

HOW DO CONTRAPOSITIVES WORK?

and again.

>>2039100
50%.

Apparently some people are not aware that coins flipped simultaneously do not interact with one another.

>>2039116

It's amazing how fucking stupid some people are.

Once you grow a brain, read the rest of the thread to learn how you're an idiot.

I just flipped a coin. What are the chances that Bender stole it?

>>2039116
Fine, test it yourself.

The only way to reproduce this irl is to record coin flips and ignore the result TT every time it comes up.

If you do this enough you'll get heads and tails (either way round) twice as much as double heads.

>>2039130
Depends when, but right now somewhere close to 0.02.

>>2039116
out of 60 that had at least one head, I got 21 which were both heads.

What is a GOOD science forum? I swear 90% of /sci/ are fucking retarded 14 year olds.

It's 1/3 btw.

If you flip 99 coins and they're all heads, what's the odds the 100th coin is heads? Flipping the last coin won't give a 1/100 chance of being heads, but 50/50.

>>2039184

If you're looking to avoid retarded 14 year olds online, good luck. We've been in an eternal september since the early 90s.

Actually, after thinking about this, I was wrong.
It actually is unambiguously 1/3.

I was originally interrupting the question in past tense (i.e. "You have flipped to coins..."), in which case I still believe the answer is .50.
However, the way it's written, you actually do have to take order into account and it IS .33...

So, my bad. Good conversation, though.

>>2039071
1/3001

or 0.000333222259%

>>2039213
*two not to

Sage for correction

>>2039184

I'd like to know this too.

>>2039223
>>2039184
Some bitter former /sci/ guys made this over the summer:

http://scichan.org/

It's slow; I haven't really checked it out yet.

tails/heads
heads/tails
heads/heads
it's either 1 of these 3
chance = 1/3
It's worded in way saying one of them will be heads, so that knocks out one of the tails/heads heads/tails options
so 1/2
if it said either one of the coins must be heads then its 1/3
tl;dr not enough information given and will make people rage like the fist of the north star over this answer.

>>2039238
It's not ambiguous at all. At least one is heads. That only eliminates TT.

>>2039267

If you'd read the thread, you'd know that crying is in no way eliminated.

The answer is 3/4


2 to the second gives 4 possible out comes

00 01 10 11

with the ones representing heads

3 head outcomes out of 4 possible.

>>2039324

oooooooo that BOTH are heads

then 1/4

flip the first coin
sit1: heads
sit2:tails
in sit 1, you then flip the next coin, 50/50 for heads. if that is heads, both are heads. if not, it is not. so you get a 50% chance for double heads with sit1.

Or with another idea of logic for sit1, there is a 50% chance that the first one was the coin that was effected by the special flip mechanic, so a bonus 50% chance of a heads. this plus the other is 100% chance for double heads in sit1, times the 50% chance of sit1 occuring, would give you 50% chance

in sit 2, since the first coin flipped tails, both cannot be heads. 0% chance for double heads.

there is a 50% chance for sit1, and a 50% chance if sit1 for double heads, so 25% chance for double heads.

There is not enough information given on the "auto head" flip mechanic to be able to determine the answer.

sorry if i forgot to edit something in this post

1/3

Stop discussing this and just read
>>2039020

>>2039366
What the hell does that prove?

>>2038988
It's the same probability as the first coin to be head, regardless of the second flip.

>>2039035
there's a distinct lack of the cylinder's diameter. assuming the general formula 4/3Pi*216 - 6Pi*r^2.

The initial volume of the sphere is 288Pi or ~14.8266714 liters

>>2040675
just now i realized the brute error i made not thinking that it's a hole and not an actual sovrapposition. after finding the cylinder volume you have to remove the part that is not comprised in the sphere.

and i don't really know a simple way of doing that.

sorry for having to deal with my retardation.

The answer is 1/3. As mentioned the only possibility eliminated is TT. TH, HT, and HH are still possible. If the questions said "What is the probability that both are heads given the first toss was H" then TT and TH would be elimated leaving HT and HH. Thus, giving 1/2. But the answer to this question is 1/3

>>2040720
>"What is the probability that both are heads given the first toss was H" then TT and TH would be elimated leaving HT and HH. Thus, giving 1/2. But the answer to this question is 1/3

lol wtf?
The answer 1/2
You said it yourself at first and then switched to 1/3 for some reason
Are we being trolled?

>>2040720
>TH, HT, and HH are still possible
TH=HT
the answer is 1/2 nigger

>>2040729

No.

"You flip two coins. At least one is heads. What is the probability both are heads?"

Possibilities:
TT (ELIMINATED)
TH
HT
HH

Probability of HH is 1/3.

Now reword it. "You flip two coins. Coin #1 lands heads. What is the probability that both are heads?"

Possibilities:
TT (ELIMINATED)
TH (ELIMINATED)
HT
HH

The probability of HH is 1/2.

>>2039035
36pi cubic inches.

>>2040754
HT and TH are the same happenstance because in this matter there is no wording that express a certain cardinality has to take place when flipping coins.

"You flip 3 coins, at least 2 are heads, what is the probability of all of the coins to land head up?"

Both the answers 1/2 and 1/8 are correct.

Regarding the original question, 1/2 and 1/4 are both acceptable, while 1/3 is not.

>>2040788
HT or TH has a probability of 1/2 though, while HH only has a probability of 1/4.

>>2040796
HT, TH, HH and TT all have 1/4 probability of happenstance.

what you're thinking of is the flip of one coin, that can yield to H or T for each individual flip.

>>2040802
Exactly. HT, TH, TT, and HH all have the same probability, 1/4. We know there's at least one head, so the possibilities are HH, TH, or HT. The probability is 1/3.

>>2040788

Just the fact you said 2 answers are acceptable shows that you do not understand the problem.

>>2040807
This is correct. This shitty problem has been going around on this board for weeks.

>>2040823

Yes. It's simply a matter of reading the problem carefully and understanding basic probability. 1/3 is the answer.

>>2040788

You can't assume HT = TH ! The coins are distinguishable. Stop with your madness.

the correct probability for this is not a 50 50 ratio but a 51 49 ratio favoring the face down side at the beginning of the flip because it has to in theory rotate less times around by half a coin turn and it lands more frequently up. then factoring in that one is already heads as in the posed question you have either a 51% chance or 49% chance

>>2040807
>>2040813
>>2040823
>>2040837

"You flip 12 coins. You know at least 11 flips are heads. what is the probability that all the flips are head?"

"You flip 12 coins. you know that 11 consecutive flips are tails. what is the probability of one flip being head?"

The two-answers-are-good situation is due to the answer being written in an awful logical manner, as it could both be asking the absolute probability of 2 flips being head (1/4) AND the probability of one of the two flip being head regardless of the other flip, for which we already know the result. it does not matter which one we are flipping, the first or the second as in we know the result of at least one of the flips.

>>2040813
> Just the fact you said 2 answers are acceptable shows that you do not understand the problem.

Your comment indicates that /you/ do not understand the problem.

Any question which includes an assertion which excludes possibilities cannot be solved without further information. Specifically, you need to know the probability of the assertion being made for each outcome before you can make use of the assertion. If you exclude "lying", then you know that the probability of the assertion "at least one is heads" being made is zero for the case where both are tails. But you don't know the other three probabilities, and thus don't have enough information to answer the question.

That's why these questions are such awesome trolling material. Different assumptions will provide different answers, and the people making the assumptions don't realise they're making them, so they're inclined to accuse anyone who comes up with a different answer of being a retard.

tl;dr: lrn2conditionalprobability.

>>2040877

Yes the question can be ambiguous, but it definitely is a conditional probability. What is the probability of 2 heads GIVEN one of the coins is heads? 1/3 as explained IN MOST OF THE ABOVE POSTS.

>>2040877
You're fucking retarded. Some people just will never understand probability.

>>2040887

I think most people are assuming fair coins. In which case, the answer is certainly 1/3.

>>2040905
"I Flipped 2 Coins. At least one is Head. What is the probability of the second coin being Head?"

Statistics has one big troll jar to pick from.

>>2040916
The probability is 1/3 as your question is stated. There are no alternative answers.

>>2040929
The answer to my question is 2/3. Test it yourself.

"I Flipped 3 Coins, at least one is Head and one Tail. what is the probability of the third coin being either Head or Tail?"

Istant trolling, just add Statistics.

>>2040938
"I Flipped 3 Coins, at least one is Head and one Tail. what is the probability of the third coin being either Head or Tail?"
1. That question has nothing to do with the previous one though.

Ran following simulation with 1 000 000 trials:
1. Flipped two coins.
2. If both tails, threw trial out.
3. Kept track of situations where I got two heads (successes) and situations where I got 1 tail and 1 head (failures).

Results: 249754 successes, 499755 failures

That's about a 1/3 success rate. Obviously if you start having thrown the first coin and gotten heads, then results will be about 1/2, but I don't think that's what the problem asked.

>>2040948
>1. Flipped two coins.
>2. If both tails, threw trial out.

Try flipping a coin, heads make a second flip, tail makes the second coin automatically heads.

run it again and count successes and failures.

>>2040977
>tail makes the second coin automatically heads.
What the fuck, why?

Everybody saying it's just 1/2 or 1/3 is wrong, read this why:
http://en.wikipedia.org/wiki/Boy_or_Girl_paradox

..
(\_/)
(x.x)
(> <)

>>2040987
because at least one of the coins has to be head, as the question dictates.

>>2040989
It's not the fucking boy girl paradox, this problem doesn't have the ambiguity in wording that it did. So stop spamming your fucking link. 1/3 is the only correct answer.

>>2040994
Which is achieved by throwing out any flips in which both coins are tails.

>>2040996
It's exactly the boy or girl paradox, how can you not see that?

Fine then. If all the anti - 1/3 trolls are such experts at probability, then surely you can refute the following.

Let X be the random variable counting the number of heads. X is a Binomial random variable with parameter 1/2.

P(X = 2 | X >= 1)
= P(X = 2 and X >= 1) / P(X >= 1)
= P(X = 2) / P(X >= 1)
= (1/4) / (3/4)
= 1/3

I think if the question were:
"One of the coins is heads"
Then the answer would be 1/2 because you assume that they have a specific coin in mind so that the other coin has a 1/2 chance of being heads.

However, the question is worded as follows:
"At least one of the coins is heads"
this means it could be one or the other so you have to consider all possibilities where at least 1 coin is heads...

Therefore the correct answer should be 1/3

A possibility is that the pair of flipped coins was selected randomly and then a true statement was made about the pair of coins and if there had been two tails in the pair, the statement would have been made that "at least one is tails". If the pair was selected as in this case, the answer to the question is 1/2.

probability of getting exactly one head after flipping two coins is .5, probability of getting exactly two heads after flipping two coins is .25. hence if you know any probability theory the answer is 1/3. people who disagree are trolls
/thread

>>2041043
>people who disagree are trolls
I think a lot of them are just stupid.

>>2041043

I think it's one-quarter trolls not one-third.

(1/2)(1/2)

>>2041048
maybe, but regardless the main reason they are posting in this thread is to troll us. sadly for them, the solution to this problem has already been proven mathematically to be 1/3.

>>2041056

(1/2)(1/2)
(1/2/2)
1/1
1

dude....

they are mutually exclusive and collectively exhaustive outcomes.


the probabilities for each individual flip multiply together for a composite event.


the probability is (1/2)(1/2)
this is not colored balls pulled from a bag.

this is not picking a collections of female/male students from a class of a specific size.


this is binomial statistics. Bernoulli trials.

>>2041062
I'll think you'll find that you need Bayes theorem

>>2041010
>P(X = 2 | X >= 1)
>X = 2 | X >= 1
> |

P(X = 2 + X >= 1)

>>2041051
2/3 imho.

>>2041062
I've never seen anyone troll themselves before.

>>2041065
Or just common sense: there are four possible, equally likely, outcomes HH TT HT TH. Discard TT as this is no longer a possible answer. This leaves a probability of 1/3. Try it in a computer script- it works

>>2041061

stupidest thing i've read all day

>>>/b/286578695

lol'd

>>2041081
Common sense dictates that we know at least one of the outcomes, leaving us with the other flip being either Tail (for HT AND TH) or Head (for HH). It's only one of the coins we need to take into account, since we already know the other coin's outcome.

Hence 1/2.

Someday someone will prove 1/2 and 1/3 are both wrong and the hilarity will ensue.

>>2041093
AHAH OH WOW

so much stupidity.
people already explained, why don't you little faggots just read those fucking posts?

You flip two coins. At least one is heads. What is the probability that both are heads?
Answer: 1/3

You flip two coins. First one is heads. What is the probability that both are heads?
Answer: 1/2

Simple as that.

>>2038988
Since we're flipping two distinctly different coins, there are three options:
Heads, then heads.
Tails, then heads.
and Heads, then tails.
So 33%.

P(both are heads|At least one of them is heads) =
(Number of outcomes with both being heads and at least one being heads) divided by (Number of outcomes with at least one being heads)

Outcomes with at least one being heads:
HT
HH
TH

Outcomes with both being heads and at least one being heads
HH

1/3 = One third or 0.333333333333333recuring

Also freakish cooincidence my captcha is 2:1 marks, 2:1 being the answer to this question and Marks being german coinage

>>2041092

>>2041102
Yes but we don't know which coin we've been told about. It could be the first or the second coin. The question doesn't specify. Therefore you can't just account for one coin.

>>2041102
But the probability that the coins were different is 1/2. The probability that they were HH is 1/4. So (1/4)/(1/4+1/2)=1/3.

>>2041105
You flip an infinite amount of coins. At least one is head. What is the probability of all being heads?

You flip the same coin an infinite amount of times. at least once it lands heads. what is the probability of it landing heads every time?

>>2041114
>P(both are heads + At least one of them is heads) = {(H,H,1), (H,H,2), (H,T,2),(T,H,2)} = 1/2

This coin problem is easy, Try this one:

You have 3 doors, behind each is a goat. You pick a door. Some guy opens another door to reveal a goat. If you change your descion are you more likely to pick the door with a car behind it?

>>2041131
smalltime, you have twice as much probability to find the car if you switch door.

>>2041131
Yes, 2/3 probability of getting the car if you switch.

>>2041121

it is obvious you have never taken a course on probability, i suggest you search the internet for a formal proof instead wasting your time trying to disprove something that has already been proven mathematically

>>2041142
technically, only 1/2. taken into account, you change your initial probability from 1/3 to 1/2 when you decide to switch, but it keeps being 1/3 if you keep your choice.

If you had n doors with n-1 goats behind them and 1 car, you would have 1/n-2 chances to find a car instead of 1/n-1 if you change your decision instead of keeping the door. but the whole thing is bullshit, until you open the door there is a car and both goats behind it.

>>2041146
don't have time for it, have differential calculus and i'm arleady behind schedule for it. but at least i'm not gonna be an engineer.

>>2041121
>implying infinity is a number

>>2041156
>technically, only 1/2. taken into account, you change your initial probability from 1/3 to 1/2 when you decide to switch, but it keeps being 1/3 if you keep your choice.
No. The probability of getting the car is 2/3 if you switch and 1/3 if you don't.

>>2041121
>>">P(both are heads + At least one of them is heads) = {(H,H,1), (H,H,2), (H,T,2),(T,H,2)} = 1/2"

No

"|" means given.
To determine the odds of X GIVEN Y You divide the possible outcomes that forfill BOTH X AND Y by the number of outcomes that forfill Y

List ALL the outcomes for two rolled coins

Coin1 Coin 2
Heads Heads or HH
Heads Tails or HT
Tails Heads or TH
Tails Tails or TT

HH forfillsboth heads and at least one is heads
HT forfills at least one is heads but not both are heads
TH forfills at least one is heads but not both are heads
TT forfills niether both heads nor at least one is heads
The number of outcomes that forfill BOTH that they are both being heads AND that at least one is heads is one (HH).
The number of outcomes that forfill at least one is heads is three (HH, HT, TH)
:. P(bothareheads|at least one is heads) = 1/3

Pic related, It's you

the bus arrives every 15 minutes, stays for 2mins and leaves the stop. you go to the stop at a random time when the bus is running, what's your chance of catching the bus?

a man shoots eight times and hits the target four times, what's the chance that three of the four hits are consecutive, provided that all combinations are equally possible?

seven men are to divide ten gems, what's the total possible plans of division?

five balls marked 1-5 are to put in five boxes marked 1-5 randomly, what's the chance that exactly two of the numbers match?

>>2041131
>You have 3 doors, behind each is a goat. You pick a door. Some guy opens another door to reveal a goat. If you change your descion are you more likely to pick the door with a car behind it?
>You have 3 doors, behind each is a goat. You pick a door. Some guy opens another door to reveal a goat.
>You have 3 doors, behind each is a goat. You pick a door.
>behind each is a goat.

Probablity of picking the door with a car behind it given that they only have goats = ZERO

>>2041179
2/17
3/14
282,475,249 (assuming gems are different)
1/6

>>2041188
Oops, 2/15 for the first one. Derp.

>>2041179
The 7men10gems question:
Infinate, provided that they can split the gems into fractions or use some sort of timeshare system

>>2041199
>implying a gem can be broken into infinitely many parts

>>2041179
15 minute bus one
You can't do it, true randomness is impossible, the closest you can get is puesdorandom, if you arrive at the bustop at a puesdorandom time the chance will be close to 2/15 but very very very very very very very very very very very slightly off. But only by powers of powers of ten though.

>>2041179
2/15
derp, dunno.
infinite, given the gem can be fractioned. wild guess 7!! for whole gems.
god damn i have no idea. 1/18?

This thread is shit ~de geso

Y'all been trolled.

>>2041202
Ok it is finite distribution, but given the uiniverses curent age of 13.75 billion years minimuim size in all directions of 6.191259 x 10^34 meters, and total engery of aproximtately 1.7 x 10^7 joules. with the planc lenghts and shit you get the picture as the number of possible combinations of 10 gems made from increments of 1 joule in space time

Since both 1/3 and 1/2 are correct answers, the REAL answer is precisely in between:

(1/3 + 1/2)/2 = 5/12