/sci/ - Science & Math

>>10855871
hurr durr independent trials, it is 50%
>you have 2 children. at least one of them is a girl. assuming a 50% chance of being born a boy or a girl, what is the probability both children are girls?
exact same shit

>>10855876
Based and redpilled, what I was thinking

Assume first hit is crit
then second hit is 50%

Assume first hit is not a crit.
First hit has 50% of crit
second has 100% of crit therefore its 50%

is this bait?

>>10855876
no thats wrong u dont multiply then probabilities.

It is 3/4 or 75% chance of both hits being critical.

>>10855871
its literally 1/3
n = not crit
c = crit
>You hit an enemy twice.
4 possibilities:
nn nc
cn cc
>Assuming a 50% crit chance,
possibility has a equal chance
>At least one of the hits is a crit.
so that leaves:
nc
cn
cc
they still all have an equal chance
>what is the probability both hits are crits?
1/3

>>10855932
no, because n and c have equal probability, so nc occurs as often as the other two possibilities put together

1.
n 50%
c 50%

2.
nc 50%
cn 25%
cc 25%

>>10855976
3000 trials

We should have 750 CC, CN, NC, and NN. There are three cases where there is at least one crit. So 2250 total where there is one crit. But there is only 750 that are CC.

750/2250 = 1/3. Any further argument from you is futile

>>10855976
100% or 0%, depending on the outcome.

>>10855976
50% is the probability that ONE of them is a crit, not that both of them are crits given that at least one of them is a crit.

>>10855871
50%, either happens or it doesn't.

>>10855992
Your simulation wrongly assumes that the crits are independent.
Any further argument from you is futile.

>>10856007
Flip a coin twice, a thousand times. You will end up with

250 HH
250 HT
250 TH
250 TT

Go ahead, I'll wait

>this thread again
Get a life you boring faggots.

>>10856021
Flip a coin by the following rules:
If H, flip for H/T.
If T, take the value of H for the second flip.

500 TH
250 HT
250 HH

Go ahead, I'll wait.

>>10856024
Why are you adding that parameter? It's not in the original problem

>>10855871
How the fuck is everyone having so much trouble with this?

HH
HT
TH
TT

are the only options, each with a .25 chance of being reached with two flips. 3 of these results have at least one hit, and 1 has two hits, so (1*.25)/(3*.25)=1/3

A = At least one crit
B = Both hits crit

P(A) = 3/4
P(B) = 1/4
P(A | B) = 1

P(B | A) = P(A | B)*P(B)/P(A) = (1/4)/(3/4)=1/3

1/3

im quite sure its 25%,
you have 50% for the first attack, and in that case it doesnt matter what comes next, since you have to get the probability of both and you can reach that only if you have the first and second a crit, which is 1/2 * 1/2 = 0.25

>>10856024
>>>10856021
>Flip a coin by the following rules:
>If H, flip for H/T.
>If T, take the value of H for the second flip.
>
>500 TH
>250 HT
>250 HH
>
>Go ahead, I'll wait.


pretty much that

>>10855876
>next hit remembers if previous hit was a crit

>>10855995
based

>you flip a coin twice
>at least one flip is heads
>it's a coin
>what is the probability both flips are heads

>>10855932
>>10856062


everyone else in this thread is either trolling or retarded

>>10855874
>you have 2 children. at least one of them is a girl. assuming a 50% chance of being born a boy or a girl, what is the probability both children are girls?
25%.
>exact same shit
Yes, this is correct.

>>10855871
this is how i see it.

>>10855874
learn how to condition, faggot

>>10855874
Personally I'm just waiting for a /pol/tard to falseflag and get triggered by "boy or girl"

>>10855871
https://en.wikipedia.org/wiki/Gambler%27s_fallacy

>>10855871
>There's x chance something happens in a series of length n.
>You know what happens in all occurrences n-1, so what's the probability of a particular series you've already predicted n-1 occurrences of?

It's quite obviously chance x. The rest has already happened.

>>10855871
>You hit an enemy twice. At least one of the hits is a crit. Assuming a 50% crit chance, what is the probability NONE hits are crits?

I'm guessing you 25% fags are thinking the probability is 25% here as well?

>>10855871
50/100 * 50/100 = 25/100 = 25% of chance both are critcs

>>10856948
That would be correct.

I really hope the majority of that ~80% are trolling.

>>10855992
Can and no are the same

>>10856221
Why ignore the possibility you of no crit twice?

>>10855871
1/3

This is /sci/ these days? People calculating 25% on a question with 3 choices? Are you for fucking real?

Two normal hits isn't possible. This leads to the aforementioned 3 choices:
NC
CN
CC

How do you get 25 from this? Or 50? NN isn't possible; stop including it.

It's clearly 1/3

>>10857092
Now the chance of a crit isn’t 50% though. You have it as 66.66%

>>10855871
https://jsfiddle.net/3o5ew9Lm/15/

Well... It's hard to argue with the code.

>>10857045
Because the problem states that there is at least one crit

>>10857094
That's conditional probability, baby

>>10857095
>Math.random()
>javascript
are you serious? At least you didn't run it on IE

>>10856062
>>10855871
>>10857095
Fucking 1/3 fags
There is a chance of not criting at all read the question properly brainlets

>>10857168
Yes, but we know that in this instance, that didn't happen, so we eliminate that possibility. Hence, we are left with three equally likely outcomes, of which one (out of three) is favourable.

>>10857171
nc and cn is the same
It doesnt matter the order you crit in since you are garenteed to crit atleast once. Therefore making it a 50% chance to cc since you “crit atleast once”.

>>10857185
So in your world do you always crit the first hit and the second is 50-50 or do you always crit the second hit and the first is 50-50.

>>10857185
>nc and cn is the same
But taken together they are twice as likely to occur as CC.

>>10855871
The question is ambiguous since we don't know how you determined at least one is a crit.

>>10857150
>>Math.random()
>>javascript
Enlighten me, scriptkiddy, what would be better?

Results would be exactly the same in matlab/julia/C/brainfuck, but that can't be run and confirmed online

>>10857191
>>10857189
I see your point im retarded

>>10857201
You determined it by being given the information.

>>10855871
0%

Prove me wrong.

Who else 0% big brain here?

>>10855871
>You hit an enemy twice

Will i hit an enemy twice, or am i analyzing the result after I've hit the enemy twice? The probabilities are different for each one.

If it's in future tense: the next strike will always be 50% chance crit/hit. The one before has already been decided (it's a crit) = the only hit which matters is the one which is about to occur. Either I get crit, or hit.

In past tense: Here all the possibilities of strikes can be analyzed in one large set, which will yield that it's 33% chance to get crit-crit.

Like >>10857201 is saying, the question lacks information.

4 possible states with equal distribution... What could be the chance? I have no idea.

55%?

>>10857259
3 possible

>>10857286
No...

Two hits
Two states per hit with 50% probability.

4 states.

>>10857341
>>10857286
1 hit 50% second hit 50% therefore together it's
50%
x50%
____
55%

>>10857345
*55%% to be correct.

>>10857341
Read OP again. There can't be 2 non crits. So that possibility gets removed.

>>10855871

C-Crit
NC-No Crit

Prior choices, all equally probable:

NC, NC
C, NC
NC, C
C, C

At least one is Crit eliminates first option, so we have:

C, NC
NC, C
C, C

One out of three is double Crit. 1/3 chance you dinguses.

>>10857354
Wrong.

Answer is 0%.

see >>10857235

>>10856038
answer this. the problem clearly describes a situation where one crit is given, so the subset nn, nc, cn.

>>10857357
I assumed that 50% Crit chance meant for each hit.

And if you assume that 50% Crit chance refers to the whole trial then that isn't correct either.

Let's say total probability from trial has 1/2 chance of getting at least one Crit. Then assuming the chance Crits of each hit are independent. We have:

p^2+p*(1-p)+(1-p)*p=1/2

Which solving gives us:

p=0.2929...

And double crit chance would be, given we have atleast one crit:

p^2/(1/2)=0.1715...

>>10856942
you don’t know the complete series tho, you are only limited in what series are viable.

>>10857385
>I assumed that 50% Crit chance meant for each hit.
me too

>Then assuming the chance Crits of each hit are independent
You can't make this assumption because of the rule that there can't be two non-crits. That's the whole point.

>>10857398
There's no RULE that there can't be two noncrits. They're just saying that, this particular time you hit your friend, there was at least one crit.

>>10857405
fuk

>>10857218
How the information was obtained determines the probability. If the person who gave you the information did not see the first hit but saw the second hit and saw it was a crit, then the answer is 1/2. If they saw both hits then the answer is 1/3.

Anyone who answered anything else than 33.(3)% should kill himself.

>>10857248
That's not what I'm saying. See >>10857415

The results are independent so there is no such thing as guaranteed crits in the future.

>>10855871

It's a contradicting task - there might be a case where the crit chance is 100 % - then it cannot be 50 % - see pic related.

Assuming that the first swing has a 50% chance to crit, the second swing has a 50% chance to crit, and each swing has a 50% to turn into a a crit afterwards (whether it was a crit originally or not - note: we have to run the probabilities out of chronological order for this last part due to the premise not being realistic); then we can draw a probability diagram as such.
Key: ! means crit
X means not a crit

1st: 1/2 ! 1/2 X
2nd: 1/2 ! 1/2 X 1/2 ! 1/2 X
result 1/4 !! 1/2 !X 1/4 XX

So, before the final step, we end up with a 25% chance for guaranteed doublecrit, a 50% chance for a possible doublecrit, and a 25% chance for a guaranteed failure to doublecrit.
Now we run the final step on the only relevant outcomes:
2 outcomes, each with a 50% chance to turn its noncrit into a crit (creating a doublecrit) and a 50% chance to turn its crit into a crit (meaning no doublecrit).
1/2 times 2 = 1 So 1 of these 2 outcomes becomes a doublecrit and the other does not. Now we can add up all our outcomes:
2/4 outcomes doublecrit
2/4 dont doublecrit
>tl;dr Its a 50% chance
I bet 99% of the motherfuckers in this thread never even took one statistics class.

>>10857441
Why is the right-leg so fucked up?

Assuming that the first swing has a 50% chance to crit, the second swing has a 50% chance to crit, and each swing has a 50% to turn into a a crit afterwards (whether it was a crit originally or not - note: we have to run the probabilities out of chronological order for this last part due to the premise not being realistic); then we can draw a probability diagram as such.
>Key:
! means crit
X means not a crit

1st: .........1/2 ! .................. 1/2 X
2nd: ..1/2 ! ....1/2 X .....1/2 ! ......1/2 X
result: 1/4 !! .........1/2 !X .........1/4 XX

So, before the final step, we end up with a 25% chance for guaranteed doublecrit, a 50% chance for a possible doublecrit, and a 25% chance for a guaranteed failure to doublecrit.
>Now we run the final step on the only relevant outcomes:
2 outcomes, each with a 50% chance to turn its noncrit into a crit (creating a doublecrit) and a 50% chance to turn its crit into a crit (meaning no doublecrit).
1/2 times 2 = 1 ...... So 1 of these 2 outcomes becomes a doublecrit and the other does not. Now we can add up all our outcomes:
2/4 outcomes doublecrit
2/4 dont doublecrit
>tl;dr Its a 50% chance
I bet 99% of the motherfuckers in this thread never even took one statistics class.

>>10857415
There is no person telling you in this problem. There is an omniscient narrator.

>>10857441
Interesting interpretation of the OP...
You are saying that by "At least 1 swing is a hit" it actually means "if the first swing is not a crit, the second swing will be". I dont think this is the correct interpretation, however, because then that sentence would be nothing more than a red herring, as it has no bearing on the probability of a doublecrit. It is worth keeping in mind, though, that this is a bait thread and the OP is intentionally ambiguous to facilitate arguments. If we take your interpretation as correct, however, then yes, it would be a 25% chance to doublecrit.

We know it wasn't noncrit + noncrit because at least one was a crit, so it's either crit + noncrit, noncrit + crit, or crit + crit. 1/3 of those is both crits.

1/2 * 1/2 = 1/4

The "at least one of the hits is a crit" is a distraction and should be ignored.

I unironically believe it's 50% and I don't care if that makes me look retarded.

We know one of them is guaranteed to be a crit so you only need to look at the probability of 1 bullet being a critical hit.

>>10855871
Yes. If second hit is 50% likely to be the critical than for fucking sure.

So we have 50% chance, that first hit is critical.
Therefore second hit with 50% possibility to be critical, even if we satisfy this.

Therefore we have 1/4 chance to get critical on both hits.

Answer doesn't change if one hit is 100% critical, because fuck you, that's why.

With second hit being the one critical, you probably won't get two hits being critical. Like literaly won't.

>>10857526
You look retarded.

>you only need to look at the probability of 1 bullet being a critical hit.
And if you did that correctly you'd get 33.33..%

>>10855871
Autism and organic food is causing global warming.

>>10857509
Is it really this simple?

>>10857528
>So we have 50% chance, that first hit is critical.
wrong

>>10857538
Yes probability works like that...

You just divide 1 by number of possible choices.

Therefore your sex is 33% probably to be "rather not to say".

And if you keep being stupid like this, we're going to reach that numbers.

>>10857547
>You just divide 1 by number of possible choices.
Thats not how stat works at all. Please draw out a probability tree to extrapolate your point.

>>10857555
It is how it works when each possibility is equally likely, which they are.

Do they not teach conditional probability in college anymore? Jesus Christ

>>10855871
I have an ability that gives every other swing a guaranteed crit chance, otherwise no crit. This is consistent with the given information. The probability that both hits are crits is zero.

>>10857531
You're right, anon. I was retarded, but I had to see for myself before I believed.

>>10857617
>It is how it works when each possibility is equally likely
but they arent
>>10857623
they do, its most of the people here havent been because this board is where 10 year olds go to feel smart.

>>10857640
>Javascript
disgusting

>>10857526
Then you leave out the case where there was a critical hit on the 2nd shot but not the 1st.

>>10857654
It easiest to play around with because you can just test things in your browser console, anon.

There's three possible paths.

Crit --> Crit

No Crit --> Crit

Crit --> No Crit

Only 1 out of the 3 possible paths produces a double crit, therefore there is a 1 in 3 chance.

>>10857646
They are. Each element of the total sample space {(N,N) , (N,C) , (C,N) , (C,C)} starts out equally likely. The condition that at least one crit is present eliminates one element, but doesn't change the fact that the remaining three are equally likely.

>>10855871
33%?

>>10855976
>2.
>nc 50% <<<<wat
>cn 25%
>cc 25%

>>10857682
>>10857680
You are mistakenly assuming that 1/4 of the outcomes magically disappear, which is not realistic. You cant change the probability of the first swing after the fact, meaning if the first swing was not a crit, then the second swing must be a crit.

First swing: .....1/2 c ................1/2 n
Second: .....1/2 c ..1/2 n .....1/2 c ..1/2 n
Probability: 1/4 cc 1/4 cn ..1/4 nc ..1/4 nn
nn cant exist, so it changes to 0/4, meaning nc must be 1/2
Then you are left with 1/4 cc, 1/4 cn, 1/2 nc. Meaning the answer is 1/4 cc.

If you disagree, draw out your probability tree.

>>10857767
So you think we can't "magically" ignore outcomes which are expressly discounted by the problem but we can actually magically force the outcome of a coin flip based on the outcome of a previous coin flip?

>>10857488
There is a person telling you the problem, using ambiguous language.

>>10857662
>not having an IDE ready to go at all times.
disgusting

>>10857767
>meaning nc must be 1/2
This is where you're making your mistake. The condition that nn doesn't happen trivially does make its probability 0. However, that doesn't magically change the relative probabilities of the other three. They remain equally likely.

You can think of the condition as a filter which blocks out the nn cases from the unconditional problem. First imagine the unconditional case. You might for instance have 100 total trials, of which there are 25 of each permutation, following from the 50% crit chance. Now the conditional filter blocks out the nn cases, leaving 25 for each of the remaining cases out of 75 total cases. This is 1/3 for each, including cc.

>>10857767
If you really know conditional probability, you should know how Bayes' theorem works. I used it earlier in this thread: >>10856062

>>10855871
You can just use conditional probability to prove it without an argument. Just let C be the number of crits. Clearly it can only be 0, 1 or 2. Then [math] P(C = 2 / C \geq 1) = \frac{P(C = 2 \land C \geq 1)}{P(C \geq 1)} = \frac{0.5^2}{0.75} = \frac{1}{3} [/math]

>>10857777
>expressly discounted by the problem
the problem specifically states that the probability of a random crit is 1/2. The part about not having nn only comes into play in the second swing.
>we can actually magically force the outcome of a coin flip based on the outcome of a previous coin flip
That is explicitly stated in the premise.
>>10857794
>They remain equally likely
Why would you think that?
>You can think of the condition as a filter which blocks out the nn cases from the unconditional problem
Why would you think it works like that? The condition that nn isnt possible would only affect the second swing, not the first swing (which is expressly stated in the premise as being 1/2 crit 1/2 not).

>>10855871
in a videogame odds do not obey statistical expectations as there is no balancing mechanism most of the time. its not even hard to code one as its just a counter each time it happens or doesnt and with a sliding scale on likelyhood when it comes of the random number generator each attempt.so you dont get a crit on a 50% chance it switches after togling a bool or adding to a int and that forces the if statement to use version B of the numebr set for if it happened on the next one and you still dont get it it does it again and shifts to version c number set. each number set has more numbers counted as being a crit than the last. alternately this can work the otehr way so you get 3 in a row but its 50% now the odds are very low with maybe 1 number in 50 that it will happen. its actually pretty simple. i coded something like this in a unity project

but nobody really cares about that and a 71% chance to occur can be more like 1/3 in a game and a 50% can seem like 90% in short streaks. so the real question is what game did this happen in? is this wow? which expansion? a turn based rpg like suikoden 2? what game nigger?

>>10857812
>Bayes' theorem is a formula that describes how to update the probabilities of hypotheses when given evidence
We have no evidence, therefore bayes theorem cant be applied.

>>10857415
Why would you assume this unless the problem stipulated that you do not know what the first hit was?

>>10857833
Because that's how conditional probability works. See the Bayes' Theorem post: >>10856062

>>10857767
Do this, anon. Flip a coin twice and only record the results if you get at least one tails like this:

TH
HT
TT
TT
HT
HT
TH

Do this a 100 or so times and then count the number of double tails you got and divide it by the total number of recorded data, you will see it's closer to 1/3 than 1/4.

>>10857853
Do this, anon. Flip a coin twice and if you get HH, change one of the Hs to a T at random.

Do this a 100 or so times and then count the number of double tails you got and divide it by the total number of recorded data, you will see it's closer to 1/4 than 1/3.

You are a biologist traveling through a rainforest when you are bitten by a venomous snake. Luckily the antidote to this venom is secreted on the back of the male of a certain species of frog native to this rainforest. You also know females and males exist in equal proportion and appear indistinguishable aside from the fact that females croak but males do not. Amazingly, you see a frog of this species sitting silently in front of you. You then hear a croak behind you and turn around to see a pair of these frogs sitting behind you. Knowing that you only have enough time to run to the lone frog or to the pair to lick their backs, which direction do you run and what is your chance of survival?

https://strawpoll.com/57z67f1h

>>10857555
Look, there is coin with 3 sides... You toss it, probability it lands on one side is 1/3.

That's how universe works.

I ran a simulation over 100000000 trials. I counted every time both were coins and every time at least one was.
Result was:
25004629/74995487
Which is approximately one third

>>10857540
Explain.

>>10857869
>Flip a coin twice and if you get HH, change one of the Hs to a T at random.
there's your problem

>>10857869
That's because you're randomly reassigning one of the H's in the HH pairs, which artificially inflate the number of TH,s & HT's vs. TT's. What should be done with each HH pair is both should be reflipped at the same time, to allow for the possibility of a TT occurring.Then, you divide and find that the probability is...

>>10857889
>you're randomly reassigning one of the H's in the HH pairs, which artificially inflate the number of TH,s & HT's vs. TT's
Thats what the special condition in the OP states should happen.

>>10857878
You know that there is at least 1 female behind you, meaning that behind you there is a 50% chance that the other frog is a male and a 50% chance the frog in front of you is a male. There is no difference in survival chance in either direction.

>>10857899
No, it certainly doesn't. You should read through this: https://en.wikipedia.org/wiki/Conditional_probability

>>10857878
hell fresh tallglassofwater

>>10857910
>meaning that behind you there is a 50% chance that the other frog is a male and a 50% chance the frog in front of you is a male.
That could only be true if the chance of a female frog croaking while you were listening was 0. The fact that the frog was sitting there silently makes it more likely the frog is male.

>>10857899
If you randomly reassign one of the H's in an HH pair, then you have to give the second H a 50% chance to flip to a T. Otherwise, you're artificially saying that each case of HH is really a case of TH/HT. That's wrong. You need to chance the possibility of TT as well for a valid statistical trial.

Imagine if you ran this coin flipping trial, and kept a tally for HT/TH vs. TT. In the case that >>10857869 was proposing, each HT, TH, AND HH would ALL be marked in the HT/TH list, whereas only TT's would be marked in the TT box. Even though HH is an impossible outcome. Think about it for a bit.

>>10855874
Depends how we know that one is a crit, obviously

>>10857878
So, if I run over to the two frogs behind me, do I have time to lick both?

>>10855871
Depends on game mechanism of enforcing 1 in two criticals.

>>10857934
>If you randomly reassign one of the H's in an HH pair, then you have to give the second H a 50% chance to flip to a T.
Is this what brain damage looks like? How do I avoid this happening to me?

>>10857839
In videogames, when you roll 1-99 10000 times, then you roll 1-100, you get 100 rolled.

>>10855976
That's literally what he said retard

>>10857941
Unfortunately, you're too far gone. You've a low aptitude to begin with and are too misanthropic to learn that you're wrong from someone else.

>>10855995
Truly redpilled

>>10856021
Highly improbable
Someone should calculate the probability of that exact outcome. It will be a few percent at best

>>10857840
You have to learn what the vocabulary means. In the context of conditional probability, the statement "there is at least one crit" is an example of evidence.

>>10856051
Its because its an ambigious question just like the distribution in order of operations troll threads. It doesnt specify how we know that at least one is what we want. It could be that we just look at the first and havent checked the second yet in which case it is 50% or it could be where we ask an omniscient observer if at least one is what we want and he says yes in which case its 1/3.

>>10857939
Yes.

>>10857839
You should learn how pseudorandom number generators work

>>10857974
In any statistics course ever, the latter interpretation would be assumed. If the former was intended, it would be explicitly stated that way.

>>10857988
I'd lick 'em both, then.

>>10857995
This is 4chan not a statistics course

>>10857974
Stop trolling, you're ruining lifes.

>>10858014
Kek

>>10855874
>what is the probability both children are girls?
100%. All boys are groomed to be trannies nowadays.

Sure is samefag in here.

>>10858016
Sure, you are pharmacist, right?

>>10858029
No, fuck the pharmaceutical industry. It's a scam

>>10858017
>implying trannies are girls

>>10855871
Hey, let's run a simulation of the problem

>ugly code
Don't want to think about optimization. This is easy to digest and has all the comments you need to understand every step, fuck you.

>>10858000
Why?

>>10858128
Because they taste good, and 66.6% odds are better than 50%

>>10858095
You did it wrong.

>>10857640 did it right.

>>10858095
>Problem says 50% crit chance
>A line chooses between 100% and 50% crit chance
Anon, I...

>>10858095
>This is how CS majors think

>>10858095
>Jokes on you, I was only pretending to be retarded

Also, I understood my mistake the second I posted. I accept all the consequences lol.

>>10858142
It's the same chance of survival in either direction and it must be higher than 50% since a frog you didn't hear croak is more likely to be male than female. Since the croak had to come from a specific frog, the other frog is equally likely to be Male as the lone frog.

I just tested it IRL, it's 1/3, you guys can stop arguing now.

>>10858252
You tested one interpretation of an ambiguous statement.

>>10855871
If P(A∩B) = P(A) and P(B∩A) = P(B)

P(A) = 50% , and the remainder independent event P(B) = 50%. Therefore , the probability of both evens happening is 50%.

Guys think of coin flipping , just because you throw heads once doesn't mean the next heads is more or less likely.

>>10858095
I sometimes get depressed and believe that despite my achievements, I am not actually that much more intelligent than other people. The fact that there are humans that cannot solve probability problems not even by brute-forcing them with a machine stronger than the one that put us on the moon gives me hope that maybe I am smarter.

>>10858252
> I just tested it IRL
There's a good chance that this post was made my an engineer or computer science major.

>>10858352
I'm glad /sci/'s incompetence restores faith within yourself, because like what the hell this thread is Boomer Facebook comments teir.

>>10858311
The statement is not ambiguous, you're just stupid.

>>10858371
Then please explain how you can tell whether this statement is telling us information about both hits or just one hit.

>>10858390
>At least one of the hits is a crit.

>>10858371
It is ambiguous because it doesnt tell us how it will ensure one of the hits is a crit.

>>10858399
Scenario1: I know you hit twice but I only saw your second hit and it was a crit. This means at least one of the two hits was a crit.

Scenario 2: I know you hit twice and I saw both hits. The total number of crits was not 0. This means at least 1 of the two hits was a crit.

Notice how both scenarios lead to the same information given in the problem. Yet the probabily of two crits is different depending on which scenario led to that information. Therefore the question is ambiguous.

>>10855871
25%, go back to school

>>10858436
If it was scenario 1, it should say so since that's more specific than scenario 2.

>>10858476
That's like saying the second scenario has more information that should have been included in the problem.

>>10858489
What? It would be the other way around. Scenario 1 has more information which should be included. Scenario 2 is the much more natural assumption, the one which is taken in statistics textbooks.

>people are literally so math illiterate they use sequential ordering to change the probability of what is essentially a single coinflip

I just assume everyone is baiting whenever this is posted.

>>10858354
>yeah just drew it up in CAD, it's 1/3
>can I have my six figures now?
fucking engineershits

>>10858493
In scenario 2 the observer knows exactly the number of crits but is only telling you part of that information.

>>10856097
according to the OP's phrasing, it does

>>10858685
Where?

>>10858690
>At least one of the hits is a crit
So either we are looking at this a posteriori, in which case 25% is correct, or we are looking at it a priori, in which case it is bayesian and they are not independent (resulting in 0.33)

>>10858693
There's no way to get 25%. Regardless of whether it already occurred or is describing a hypothetical situation in the future it's still the same problem. The ambiguity is in the interpretation of "at least one is a crit" since how this information was obtained determines the probability. I don't know why half of /sci/ always interprets "X occurs" as "X must occur" when calculating conditional probabilities. It's retarded.

>>10858095
>the weapon somehow remembers its last hit

>>10855876

This is wrong, because it doesn't assume the knowledge of knowing that at least one hit is a crit. You need to apply Bayes theorem in this case.

imagine getting anything other than 1/3

>only 18.54% of people got the right answer

Just fucking lol

>>10858920
most of the board is made up by high schoolers (retarded zoomers) so that's not surprising

>>10858920
You mean 0.82%

https://en.wikipedia.org/wiki/Boy_or_Girl_paradox

>Gardner initially gave the answers 1/2 and 1/3, respectively, but later acknowledged that the second question was ambiguous.[3] Its answer could be 1/2, depending on what more information is available beyond that you found out just that one child was a boy. The ambiguity, depending on the exact wording and possible assumptions, was confirmed by Bar-Hillel and Falk,[4] and Nickerson.[5]

>>10858920
>thinking the one with 18% of the vote is the right answer.

Just fucking lol

>>10859097
there's nothing ambiguous it's plain english. i suggest investing in a dictionary

>>10859098
based retard

>>10859099
Can you read, retard?

https://en.wikipedia.org/wiki/Boy_or_Girl_paradox#Analysis_of_the_ambiguity

>>10858095
legitimately retarded

>>10858343
>0.5*0.5=0.5

>>10859153
When did i say you ever multiply it you fucking square. They are independent events and therefore are the same probability of event a or b.

>>10859157
>independent events
https://youtu.be/-YqL0TQnvFI?t=8m

>>10859167
oh jesus chirst i meant this

P(A|B) = P(A)

P(B|A) = P(B)


kill me and i apologize for calling you a square

>>10858095
>>10857640
why do I feel like the only sober girl at the party?

>>10855871
100%

I have a high luck stat

>>10857974
>It could be that we just look at the first and havent checked the second yet
nobody that is not an insufferable cunt would ever phrase it like this in that case

>>10859213
Sure they would.

>>10855871
Because the problem references crits it is either a video game or a ttrpg.
The actual way to produce a result in game is to roll for first hit damage and first hit crit then if the first was a crit you do the same for the second but if the first didn't crit you just roll the damage for the second hit because it is a guaranteed crit right?

So 50-50 first hit crit then branching 50-50 second hit crit.

Total result is 50% regular then crit 25% crit then regular and 25% two crits.

>>10857821
This. Thanks anon

>>10859236
>guaranteed crit
Nothing is guaranteed.

>>10859253
It works like this in some loot box mechanics where you are guaranteed a gold or epic or whatever for every X rolls. It just means roll X is conditional on the results of the previous X-1 rolls.

>>10857095
All these "the code proves it" arguments are bullshit. I mean 1/3 is the right answer but your code is based upon your assumptions

>>10859259
well in this case the conditional just restricts the modelspace to those models where at least one of the two hits is a crit.
and then the probability is simply the probability of those models which satisfies "two crits"

no silly guaranteeds or whatever

>>10855871
>at least one of the hits is a crit
>>10859302
>no silly guaranteeds or whatever
Seems like a guarantee to me.

>>10859309
It's not, just because an event occurs does not mean it had to occur.

>>10859320
So what if it doesn't occur?

>>10859330
What about it?

>>10859331
Then it won't be at least one crit.

>>10859337
Yes, but it happened to not be in this one instance. How is this hard to understand? If you flip a coin and get heads, do you surmise that the probability of heads is 1?

>>10855871
NC
CN
CC
NN

NN can not exist, because at least one has to crit

So, that leaves us with 3 options, reducing to a 50/50 chance; either it happens or it doesn't.

>>10859380
If only one the second hit was seen and it was a crit, then CN cannot exist either. The question is ambiguous.

25% is correct but most people posting it are mongoloids who dont explain why correctly
Atleast one hit has to be a crit
There is a 50% chance on first hit to be a nocrit, that is one branch that forces the second hit to be a crit
The second branch of a crit on first hit then runs through 50% again, resulting in either crit or no crit
NoCrit-Crit-50%
Crit-NoCrit-25%
Crit-Crit-25%
There are 3 possible results, but using your lil noggin to think past "oh 3 results, 1/3 is answer" you come to the result that there is a 25% chance of two crits.
By adding in "at least one of the hits is a crit" forces the chances to be dependent, flipping coins to follow those rules requires you to throw out results, it is not a true random chance problem as the tester edits the results

>>10857092
>How do you get 25 from this? Or 50? NN isn't possible; stop including it.
I didn't read the question properly and included it. Seems pretty obvious Anon.

>>10859253
>"Atleast one hit is a crit"
>First hit is a non-crit
>Second hit is guaranteed crit
How do you fail to understand this

>>10855871
haha

>>10859731
>second hit happened to be a crit, with a 50% chance
ftfy

>>10859432
Nothing is seen by anyone. It didn't actually happen. You are just magically given information on the crits.

Some people here seem to be under the impression that "conditional probability" doesn't mean "we'll look only at the probability of the outcome under certain circumstances" but rather "if it doesn't happen, we'll MAKE it happen"

Even Reddit could solve this problem better than /sci/. Be ashamed of yourselves.

>>10860815
>Nothing is seen by anyone.
Then how do we know the hit was a crit?

>It didn't actually happen.
Whether it happened or we are talking about it theoretically happening, the outcome is the same. It's an ambiguous question.

>You are just magically given information on the crits.
This is not enough to answer the question. We need to know the chance of being given this information.

P(CC|ALOC) = P(CC) P(ALOC|CC) / P(ALOC) = (1/4)(1) / P(ALOC)

If we are told ALOC whenever there is at least one crit then P(ALOC) = (1/4)(3) and the answer is 1/3.

If we are told ALOC only when a specific hit is a crit then P(ALOC) = (1/4)(2) and the answer is 1/2.

Both situations lead to the same information being given but not to the same answer.

>>10856097
It does, the chance to crit must be at least 50%

>>10860882
So if you flip a fair coin and get tails, the next flip is guaranteed to be heads right?

>>10860821
/thread

>This whole thread
The absolute state of /sci/

>>10859349
No because I might be dreaming and it might be an illusion

>>10860887
>At least one of the hits is a crit.
You can't have 2 fails. At least one is a win.

>>10860821
The OP post doesn't say 'conditional probability'

>>10861187
But it's not a magic coin, Anon. If you get tails once it's still 50% chance at tails the next time. And when that does happen you know not to count that one. You don't get to force the situation to conform to what you need it to be because then it's not probability any more.

>>10861199
So the answer to Op is 50%:)

>>10861206
No

>>10861199
It's just paradoxically worded, because even though the chance to crit is 50%, it specifically says one of two hits crit, which makes it a definite 100% chance.
However, following the 50% chance all the way line, you get 1/3, after discounting all the non-crit events.

>>10861206
No, it's 1/3 because 2/3 it's going to be 1 crit and 1 non crit.

>>10861213
>It's just paradoxically worded, because even though the chance to crit is 50%, it specifically says one of two hits crit, which makes it a definite 100% chance.
That's not how probability works. Everything has a 100% chance of having occurred when it has already occurred. The point is you don't know what exactly has occurred and you're trying to reason how probable a certain scenario is. The only thing that's 100% definitely known to you is that at least one of the hits is a crit, after both have already occurred. That doesn't mean that was 100% likely to happen.

It's a contradictory prompt you shitstains.

>>10861187
You can, it just didn't happen in one instance. Dumbass.

>>10861213
it's 25% dickhead. see experiment: >>10859186

it's clearly 25%

We already know that one of the hits is a crit. What is the probability that the second one is also a crit? 50% of course.

Anyone answering otherwise is a moron/troll.

>>10861302
This just counts the number of times the first hit is not a crit and the second is. It has nothing to do with the question and isn't even necessary since anyone with half a brain can see that's 25% without running a simulation.

>>10861325
So? I assume that's a shortcut. If the first hit is not a crit, then it is impossible for it to be a case where both hits are crits.

CH*
CC**
HH
HC*

Its 1/3.

>>10856051
Establishing that probability matrix assumes that TT could in fact have happened, but we disregard it. We don't know that from the wording of the question.

>>10861320
>What is the probability that the second one is also a crit?
This implies that the information "at least one of the hits is a crit" is information about a specific hit. It could be information about the pair combined. For example, if I view both hits and tell you "at least one of the hits is a crit" whenever the following occur:

NC
CN
CC

Then 1/3 of the time I give you this information both hits will be crits.

But if I only look at the second hit then I will tell you "at least one of the hits is a crit" whenever the following occur:

NC
CC

Then 1/2 of the time I give you this information both hits will be crits.

The question is ambiguous.

>>10861333
>If the first hit is not a crit, then it is impossible for it to be a case where both hits are crits.
Then why are you counting it in your percentage???

>>10861353
??? it's a potential outcome

>>10861371
Please explain to me how not getting a crit and then getting a crit counts as getting two crits.

>>10861394
it doesn't which is why hit is not incremented in such a case

>>10861406
Then that means no crit and then no crit counts as a trial when it didn't occur since we know at least one hit was a crit. Moron.

>>10855995
B&r

>>10861417
but no crit no crit never happens you imbecile

>>10861477
You're counting it by counting anything which starts with no crit as a trial you mongoloid.

>>10861502
anything N we consider NC as is guaranteed. What don't you understand about this

>>10861505
>anything N we consider NC as is guaranteed.
It's not guaranteed you fucking moron, it just didn't happen in this instance. You're weighting NC as happening 50% of the time and CN as happening 25% of the time when they are equally likely to occur.

>>10861518
>It's not guaranteed
>"At least one of the hits is a crit"
OK

>>10861528
>It's guaranteed
>50% crit chance
You are a fucking retard. Just because something occurred in one instance does not mean it was guaranteed to occur.

>251 replies
I thought /sci/ was less retarded than /v/.

>>10859186
>>10861302
>writing a computer simulation makes it the truth
lmao

You can write a computer simulation to get any of the common answers (1/2, 1/3, or 1/4). The answer depends on the assumptions you make about the problem, and the assumptions you make about the problem will also inform the logic of your computer simulation. Pic related.

>>10861548
ffs
>At least one of the hits is a crit
meaning
if N, then NC
if C, then 50% chance CC, which we record
25%
you can't possibly be this dumb

>>10861549
ssh

>>10861554
>>At least one of the hits is a crit
>meaning
That's the thing, retard. It could mean more than one thing. See >>10861549 (which you replied to, but obviously didn't read).

>>10861554
>At least one of the hits is a crit
>meaning
>if N, then NC
This describes what happened, not what had to occur, moron. Not to mention that this violates the assumption stated clearly in the problem, which is that the chance of a crit is 50%, not 100% after not getting a crit. You can't possibly be this dumb.

>>10861554
So if you flip a fair coin and get heads, according to your logic the probability of getting heads is 100%

>>10861559
>At least one of the hits is a crit
if the first hit is not a crit, the second must be by way of how we construct the rules of the problem
>>10861565
if the problem says so

>>10861566
>if the problem says so
I just gave you the problem, does it say so or not?

>>10861567
from what was written, no

>>10861549
The TLDR of this image is as follows:
>If "at least one of the hits is a crit" is pre-determined by some gameplay mechanic which forces the second hit to be a crit if the first is not, the answer is 1/4.
>If "at least one of the hits is a crit" just means we are told after the fact that the number of crits was not zero, thus eliminating one of four possible outcomes, the answer is 1/3.
>If "at least one of the hits is a crit" means we looked at the result of one attack and saw that it was a crit, then the probability of two crits is just the probability of the other attack being a crit, and thus the answer is 1/2.

I'm pretty sure that 1/4 isn't intended to be one of the answers, though. The point of this bait is for people to argue over 1/2 and 1/3, because the problem is just a rephrasing of this one:
>https://en.wikipedia.org/wiki/Boy_or_Girl_paradox#Second_question

>>10861566
>if the first hit is not a crit, the second must be by way of how we construct the rules of the problem
No, if the first hit is not a crit then the second only has a 50% chance of being a crit according to the problem. Saying something occurred does not mean it is guaranteed to occur.

>>10861570
How does "at least one coin landing heads" guarantee that at least one coin lands heads but "a coin landing heads" does not guarantee that the coin lands heads? You're contradicting yourself.

>>10861574
>No, if the first hit is not a crit then the second only has a 50% chance of being a crit
if the first chance was not a crit, then how can the second not be a crit either when "at least one of the hits is a crit"?

>>10861582
nothing is contradictory. If the coin has already landed heads, then nothing further needs to be enforced to satisfy the rules

>>10855871

The Monty Hall problem tore us apart in the exact same way like I am seeing here. I'll be damned is this is another!

Here's my thought. There are two enemies in front of me. I hit each enemy one time. I can critically damage the enemy once every two punches that I throw, or 50%. This means, at random, my punches can critically hit an enemy, or not, depending on whatever cycle it's in.

So, I can strike both of them critcally, or one of them (at least one of the hits is a crit). That's 3 different options. The one option we want is when both hits are crits, which is only one out of the three options. Thus, 1/3, or 33.3%.

Now can't we all just get along?

>>10861590
There are no "rules" when it comes to coin flips. It's just probability. Hey, I just flipped two coins. At least one came up heads. What is the probability that both came up heads?

If you say 1/4 because one heads was "guaranteed" to happen, then you're a fucking retard, because I don't have magical powers and I didn't break the laws of physics during my coin flipping. I'm just telling you after the fact what happened.

The answer is 1/3 because I merely told you that at least one came up heads, i.e., it is not the case that both came up tails, i.e., one of four equally probable outcomes (HH, HT, TH, TT) is eliminated, leaving three equally probable outcomes (HH, HT, TH).

The answer would be 1/2 if I had told you that the first coin came up heads, because then I would be eliminating two possible outcomes (TH and TT) leaving only two (HH and HT). It would also be 1/2 if I had told you that the second coin came up heads, because again I would be eliminating two possible outcomes (HT and TT) leaving only two (HH and TH).

>>10861590
>if the first chance was not a crit, then how can the second not be a crit either when "at least one of the hits is a crit"?
This is like asking "if a coin lands heads how can it be fair?" Probability is not describing one event.

>nothing is contradictory. If the coin has already landed heads, then nothing further needs to be enforced to satisfy the rules
The coin landing heads has to be enforced. So according to you the coin will always land heads. Because you don't understand how probability works.

>>10861603
>>10861604
please read >>10861572
you fuckwits and stop replying to bait

>>10861607
I'm >>10861603 and what I wrote is entirely consistent with >>10861572. The reason 1/4 isn't a valid answer for coin flips is that we already know God didn't write gameplay mechanics for the universe which guarantee one heads per two coin flips. 1/4 is a valid answer for the critical hit problem only because we can imagine a game in which one of the critical hits is guaranteed, even though that would be retarded. Meanwhile, I deliberately eliminated the answer 1/2 while asking about coin flips by saying that I flipped the coins. The person solving the problem did not flip the coins and can't possibly know which coin was heads, and knowing that a particular coin was heads is the only way to get 1/2 as an answer. The reason 1/2 is a valid answer for the critical hit problem is that the problem is phrased in second person, meaning the player attempting critical hits is the one who must determine the probability, and we can imagine that the player (with first-hand knowledge of the combat) knows which hit was critical.

>>10861618
>1/4 is a valid answer for the critical hit problem only because we can imagine a game in which one of the critical hits is guaranteed, even though that would be retarded.
Why is it retarded? This could easily be a mechanic in a game.

if one of the hits is guaranteed crit, then it's a 100% chance for that hit. 1 * .5 = .5. QED.

>>10857095
Eww, just use the number of possible states. This kind of reasoning is shit

>>10861718
It would be retarded because the rules are simultaneously stating that there is a 50% critical hit chance. If the baseline critical hit chance is 50% but you're also guaranteed one critical hit every 2 hits, then the effective critical hit chance is actually greater than 50%, which means the originally stated critical hit chance is incredibly misleading. Therefore it's bad game design.

>>10855871
dumb easy. you flip a coin twice. At least one is heads what is the probability they're both heads?

25%

>>10862131
Wrong.

>>10862152
no it's not retard.

hit an enemy twice = perform a probabilistic event twice.

at lest one is a crit assuming 50% crit rate = at least one is heads or tails doesn't matter.

what is the probability both are crits = what is the probability both events are tails or heads.

it's 1/4 either way nigga.

>>10855871
>https://strawpoll.com/b59618ab
If it's fucking 33.3333...% I swear to God ffffffuuuu

>>10862165
By multiplying them you are calculating the probability of getting two heads, not the probability of getting two heads given at least one is heads. This reduces the probability space and increases the probability of two heads above 25%.

You have a certainty that one flip will be heads, so that is 100% or 2/2 chance,which is equivalent to 1. The other flip will be a 50% chance, or 1/2 chance. Consequently, and given that x×y=y×x, when multiplying consecutive flips, and because one flip is 1 and the other 1/2, the result must be a 1/2 chance, or 50%. Any other result comes from a failure to understand the question.

>>10862174
think about it this way my guy.

you are guaranteed heads

you could have

ht
th
hh

oh shit you right it's 1/3

>>10862188
That is one possible interpretation. Another is that at least one head is information about a specific coin:

th
hh

Which gives 1/2.

>>10862184
>You have a certainty that one flip will be heads
Wrong.

>>10862195
since there are two possible interpretations one 1/2 and the other 1/3 just average them and the correct answer is 5/6

>>10862218
You mean 5/12? And there are many possible interpretations.

>>10862221
how many possible interpretations are there?

just add them all up and avenge it. Not a paradox.

Bayes BTFO.

>>10862226
Potentially infinite. Also an average would be improper if the distribution of prior probabilities of interpretations is not uniform.

>>10862249
You calculated the percentage of double crits out of all cases, not the percentage of double crits out of the cases where you are told at least one hit is a crit. You fail.

>>10861593
I like this explanation, makes a lot of sense. I just hope people could see this one

>>10862255
Ah yeah I missed that. It's 50% then!

You can prove anything with math

>>10862263
oh FUG.
It is 33%.

>>10862259
Based on what?

>>10862277
Nothing, I had to re-read the question and do it properly here >>10862269
But it's obvious if you don't jump to conclusions

>>10855886
yeah its bait.
You got the answer.

>>10862279
It's ambiguous, either interpretation could be correct.

>>10862285
>you hit an enemy twice
>at least one of the hits is a crit
Either the first hit or the second hit can be a crit, not just the first.

>>10862287
It's not.

why. is this thread still going.

>>10862320
To get to the center, of the center, of it all.

>>10862320
Because the fucking question is ambiguous but people keep arguing that it's not. It's the goddamned boy/girl problem with a different name.

Either
1. You take a reference of every two hit combo you've done and check to see whether you got a crit or not. You notice one was a crit. The other has a 50% chance to be a crit.

Or
2. You check only those two hit combos where at least one hit is a crit. The chance the other hit is also a crit is 1/3.

So based on your assumption, which is not explained in the problem, you can have either answer and people are going apeshit trying to prove THEIR way is right. And on and on it goes, and on and on it goes.

>>10862354
There is no ambiguity. Your neighbor has two kids, and you see a boy come out of the house. You KNOW that at least one of them is a boy, because you just saw him walk out the house. What is the probability that both are boys? The answer is 1/3. It doesn't matter how you know that one is a boy, or heads, or a crit. You're obviously clinging to the wrong answer because you devoted too much of your ego into it and dont want to concede that you were wrong

>>10862354
>>10862429
And if you think the answer is 1/2, then you're implying that BB is as common as BG/GB which is wrong. The boy could be the oldest or the youngest.

Well let's look at the possible scenarios

1) First hit crits, which means the second hit has a 50% chance to crit
2) First hit doesn't crit, which means the secons hit crits
3) Both hits crit

The first 2 scenarios will count as 50% because it's the same result and because it doesn't matter which hit crits.

The answer is 50%.

>>10856062
Bayes'd and redpilled.

>>10862429
No. The question is ambiguous.
https://en.wikipedia.org/wiki/Boy_or_Girl_paradox

>>10862429
>Your neighbor has two kids, and you see a boy come out of the house. You KNOW that at least one of them is a boy, because you just saw him walk out the house. What is the probability that both are boys? The answer is 1/3.
It's 1/2. They're are two equally likely possibilities since you know a specific kid is a boy:

BB
BG

Since you only saw the first kid this means you would not know at least one is a boy if the kid you saw was a girl but the other kid was a boy. Only when you would know that in all three cases is the answer 1/3. How is this hard to understand?

>>10862438
>And if you think the answer is 1/2, then you're implying that BB is as common as BG/GB
No it's implying that BB is as common as BG only. GB is impossible since the first child is the one you saw.

>The boy could be the oldest or the youngest.
LOL, you don't have to order them by age, you can order them by anything and if you have information about a specific kid you should order them by that information. Otherwise you are ignoring that informations specificity.

>>10862639
Oof you're an idiot. As written, 1 contains 3 since 3 requires the first hit to be a crit. Then your argument about 50% makes no sense, they are clearly different results. Just stop posting until you understand probability.

>>10855871
Its 1/3 because conditional probability is a meme

>>10862639
I like it how you correctly figured out there are 3 options but managed to get the answer wrong anyway

Can anybody verify >>10861593 ?

>>10863339
Verify what? He's giving the correct answer to one valid interpretation of the question.

See >>10861549 >>10861572

This has been discussed to death but /sci/ is apparently no less retarded than any other board so the debate continues anyway.

>>10863409
>>10863339

I couldn't agree with you more!

>>10863339

from random import choices

def gen():
return choices(['n', 'c'], k=2)

samples = [gen() for _ in range(100000)]

samples = list(filter(lambda n: 'c' in n, samples))
crits = list(filter(lambda n: 'n' not in n, samples))


print(len(samples), len(crits), len(crits) / len(samples))

>he uses logic to figure out meme problems on /sci/ and not beginner python
I feel bad for you son

>>10855871
AAAAAAA i fell for the bait dammit

>>10856221
THis

Bumpu this smart frens thread