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How smart is /b/?
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How smart is /b/?
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>>703062403
What coins?
>>
25%
>>
1/3.
Only autistic faggots would say 1/2..
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>>703062403
The distribution of results will trend towards a probability of 50% for either binary result, with a large enough result set.
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>>703062403
50/50 faggot
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>>703062403
50% duh
you KNOW that one lands heads, you can ignore that
now you just have a 50% chance of the other coin landing heads
this isn't hard
>>
>>703062403
HH
HT
TH
TT

Because the question states that at least one must be heads, we eliminate TT.

HH
HT
TH

HH has 1/3 probability.
>>
>>703062576
And prior results do not influence future results.
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>>703062576
>>703062610
>>703062625
Retards
>>
>>703062403
P(two heads given one head) = P(two heads) / P(head for one coin) = 1/4 / (1/2) = 50%
>>
>>703062403
2/3
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>>703062648
TH = HT

why do i even bite?
>>
>>703062561
>>703062648

Fucking this
>>
>>703062796
Because HT and TH are two different possible results.
>>
>>703062403
I was told for years that even though I learned this in school it would never help me in real life?

I'll be honest, I'm still not sure I consider /b/ to be real life.
>>
>>703062403
faggots that think H, T and T, H are a different result will say 1/3

all others will say 1/2, which is objectively correct, this is not a "how you interpret the question" problem either, 1/3 is wrong. end of story
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>>703062403
1/3 muthafucker.
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>>703062796
You just went full retard
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>>703062796
>TH = HT

You're fucking retarded.
>>
>>703062854

You're retarded.
>>
>>703062796
>>703062854
>thinking TH and HT are the same
It's ok to be wrong sometimes.
>>
>>703062403
This is a take on the 3-door puzzle: you are offered a choice of 3 doors, with a car behind one of them. You pick a door, and they open one to reveal nothing, then offer you the chance to switch your pick to the other unopened one. The logic is that you should, because this increases your chance from 1/3 to 1/2. It's a something that's supposed to make mathematical sense while not making any logical sense.
>>
>>703062870
its correct. result sets are equal if they contain the same items, the order is irrelevant
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>>703062561
>>703062648
>>703062798
>>703062858
>tfw /b/ is smarter than you though
>tfw people are still confused by the Monty Hall problem
>>
>>703062403
Depends.
Did you chose which coin to reveal based on the fact that the result was heads?
>if so 1/3
Or did you reveal one at random which just so happens to be heads?
>if so 1/2
>>
>>703063034
But it does make perfect logical sense. On of the solutions was KNOWINGLY removed, not randomly.
>>
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Wow, there are people retarded enough to believe that HT = TH

Flip a penny and a quarter.

Is
penny=heads, quarter=tails
the same as
penny=tails, quarter=heads

No, of course not.

Answer is 1/3, you fucking retards.

2 coin flip. All possibilities equally likely

HH
HT
TH
TT

At least 1 landed heads, so only TT no longer possible, leaves

HH
HT
TH

HH is 1 of those 3

1 of 3

1/3

Eat a dick.
>>
>>703063157
Yeah, mb I was typing in a hurry on a phone, meant common sense
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>>703063229
This unupset me, thanks anon.
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>mfw people actually think it's 1/2
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>>703062854
Idiot.
>>
33.3%
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>>703063184
2 coin flip. All possibilities equally likely
H, H (same positive)
H, T (mixed)
T, T (same negative)

At least 1 landed heads, so only TT no longer possible, leaves
H, H (same positive)
H, T (mixed)

H, H is 1 of those 2
1 of 2

1/2

ftfy tml
>>
Damn, people are actually getting the correct answer this time.

Protip: It's not 1/2
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>>703063604

HT and TH each have an equal probability of occurring, you retarded cunt.

So if you choose to ignore that they are different outcomes, you must account for both of their probabilities, in which case you get

HH = 1/3
HT/TH = 2/3

I hope you are trolling.
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>>703063604
If we knew which coin was guaranteed to land heads, then it would be 1/2, because we'd eliminate two of the possibilities, either {TH, TT} if coin 1 is guaranteed or {HT, TT} if coin 2 is guaranteed. But because we don't know which coin is guaranteed (the question never states which coin is guaranteed), then we can't say that TH and HT are the same, and we can only eliminate the TT possibility, leaving us with 3 other possibilities {HH, HT, TH}. In that set, HH has 1/3 chance of occurring.
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>>703063819
your algebra is wrong.

you're basically listing variables in a result set, the question asks for a set of result sets, which is multi-dimensional:


{{T,H}, {H,T}, {H,H}} can be reduced to {{H,T,}, {H,H}}

listing {T,H}, {H,T} separately is redundant and every higher level math or logic teacher would let you fail the class. this is basic.
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>>703064193
HT and TH are different results which each have a probability of occurring separate from each other. Please read my posts before trying to reply to them, and don't bother replying until you graduate high-school math.
>>
>>703064193

You're retarded.

Source (Slide 4)
Washington University Math Dept
http://courses.cs.washington.edu/courses/cse312/11wi/slides/04cprob.pdf

1/3
>>
>>703064193

>the question asks for a set of result sets, which is multi-dimensional:
>multi-dimensional
>Basic conditional probability

Look at this retard trying to sound smart by talking complete bullshit.

Kill yourself.

1/3
>>
it's 1/2. because one coin is always a head, no matter what. The second either lands on heads or tails
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It depends how many times I was woken up, asked what day of the week it was, and put back to sleep.

https://www.youtube.com/watch?v=5Cqbf86jTro
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>>703062403
If one coin is designed to always be heads then the probability is 50%. But if the coins are flipped and then you are told none are tails the probability that both are heads is 1/3.
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>>703064541
Every variable is a dimension, you tin can. Lrn2fucking analysis.
>>
>>703064619

You can't even get a basic conditional probability question correct, you retarded cunt, and you want to talk about dimensions.

kek

Kill yourself.
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>>703064564
>because one coin is always a head

Which coin?
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>>703064581
The question doesn't specify that "one is designated to land on heads." It specifies that one or two of the coins lands on heads. It's actually quite clear, despite English being shitty, and this thread designed to confuse.
>>
Man, retards ITT.

Flip 2 coins. At least 1 landed heads, so you could have equal chance of

coin1=heads, coin2=tails
or
coin1=tails, coin2=heads
or
both coins heads

1/3
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>>703064780
>Which coin?
does it matter? you flip the first one. It's heads. you flip the second one, it's heads or tails.
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>>703064736
It depends how the information of it landing on heads was ascertained. Given the story problem nature of the question, it implies a scenario where two coins were flipped. One landed on heads, and the value of the remaining coin remained a variable.

This is a different chain of events than magically viewing through your future sight whether or not both would land on tails, closing that probability loop from ever occurring, and then viewing the results in real time again.

Like, we get it. It's a problem that's worded in such a way to be intentionally vague, so that there's two plausible ways of converting the English into mathematical notation. And nobody here, (except this guy

703063604

) is having trouble once it's converted into mathematical notation. It's just that English is dumb, and the way the problem is worded with English is even dumber.

How the fuck are you supposed ascertain that it's going to land on not both tails, without knowing the value of either coin? What is this, some kind of quantum erasure bullshit?

BECAUSE I WILL GO THERE IF WE'RE GONNA' START QUANTUM'ING THROUGH TIME IN THIS THREAD GORRAMNIT.
>>
>>703065272
>you flip the first one. It's heads.

But that's not what happens, retard.
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>>703065353
I mean, you tell us what happens then. Tell us in linear time how the story problem works. Start with flipping two coins. They are now in the air. Then what happens?
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>>703064342
haha, high school

check the pic related, it calculates the power set of {a,b,c}, which means all possible subsets of this set. its 8, because 2^3, but thats irrelevant

note that in the result sets, there is NO {b, a} or {c, b, a} because they are EQUIVALENT to the already listed {a, b} and {a, b, c} respectively
you do not list those sets twice (or more) because the order is irrelevant
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>>703065529
Then you cover them and a person that can see them tells you that at least one of them is heads.
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>>703065541
That's mighty fine for you, but none of that applies here. We don't know which coin will land heads up. We know the true state of your variables a b and c at all times.

Your argument is quite literally invalid.

Remember that you're not allowed here if you're under 18. Scurry off back to mommy, now.
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1/3 tards
If you care read pic related
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>>703065291
>It depends how the information of it landing on heads was ascertained.

You are fucking told at least one landed heads.

>it implies a scenario where two coins were flipped. One landed on heads, and the value of the remaining coin remained a variable.

No, faggot. BOTH coins are variable, as you have no idea which coin landed heads. So EITHER coin could be tails, just not both simultaneously. This gives us 3 equally probable outcomes all containing at least 1 heads
HH, HT, TH

>Like, we get it. It's a problem that's worded in such a way to be intentionally vague

No, it's not. It's a basic conditional probability question, you fucktard. Only retards get confused because they don't understand probability. This is the basic layout of a conditional probability question:
>what is the probability of event A given event B?

OP's question is
>What is the probability that both coins landed heads given that at least 1 coin landed heads?

So here,
Event A = both landed heads
Event B = At least 1 landed heads

SImples. Answer is 1/3
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>>703065541
But even in your pic, what you end up doing is taking the power set of P({a,b})) and just removing the null out of it, to get three possibilities.

In other words,

∅ = T,T
{a} = H,T
{b} = T,H
{a,b} = H,H
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>>703065541
>Thinking this proves you right
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>>703062403
50% the probability for any variation and and number of flips Will always be 50%
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>>703065529

They land.

I tell you at least one landed heads. Now you work out the probability that both landed heads.

Protip: It's 1/3

Why are you having difficulty with this?
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>>703065625
That's a pretty good one.

(I'm a math tutor sometimes, and I always have the most trouble explaining these things in story form, without relying on quantum mechanics...)
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>>703065658
>none of that applies here
you're the one arguing H, T is separate from T, H
you missed the point I was trying to make here
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Knowing that every /b/tard has wasted their luck on repeating digits there is 0% chance for both coins to land head.
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>>703063184
It says two coins, not two different looking coins you mouthbreathing autist.
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>>703062561
I concer.
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>>703065864
Third-ed
>>
50%

source: math major
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>>703063789
Except the probability of it being either HT or TH is based on whether the second coin (that isn't already H) is T.
Since you can't get two tails from one coin, you fucking idiot, it's 1/2.
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>>703065842
>I'm a math tutor sometimes
>I rely on quantum mechanics

Kill yourself.
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>>703065913
>>703065695
Refer to this, are you arguing with the author who has a PhD?
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>>703065992
yes i am arguing
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>>703065913
>>703065992

1/3

source: PhDs in Logic, Applied Mathematics, Analytics
>>
It's 0% those are euros, no head on them
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>>703066035
I feel like this is a bait but I'm all ears regardless since I'm a fucktard at maths
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>>703065859

You fucking retard, I used 2 different coins to illustrate to mentally deficient fucktards like you that TH is not the same as HT, WHETHER YOU USE IDENTICAL COINS OR NOT.

Jesus, how can someone be this retarded?

Kill yourself.
>>
2/3
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>>703065992
They gave someone like you a PhD when you can't even sort out basic probabilities?

>they'll give americans degrees for anything these days
>>
the trick is it says "given" so you can ignore what was said before given. what's the probability i shit myself while you shit yourself given you are already shitting yourself. the answer is whatever the probability there was for me shitting myself alone, which is 100%
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>>703065945

What the fuck are you talking about, you retard?

Filp 2 coins

first coin could be tails, second heads
or
first coin could be heads, second tails
or
both coins could be heads

All equally likely.

1/3

Eat shit and die, retard.
>>
>>703066185
>>703066086
forgot to link
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>>703066180
It's not mine, see Sheldon M. Ross
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>>703066185
>before given
meant after
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Simulation confirms 1/3
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>>703066099
Yeah but you're not looking for penny heads AND quarter heads as separate values

just heads

Don't be such a pissy little baby because you're fucking stupid

Say you don't know which of the coins is H.

You throw, it's tails, but you know one of them has to be H, so it's TH.

You throw, it's heads, and you don't know what the other coin is because it could be either.

Are you suggesting that a coin has a 1/3 chance of being heads even though there's only two sides? Or are you talking about pennies and quarters?

Remember not to think too hard or you'll get a headache like last time, dipshit
>>
100% of course
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>>703062403
I kow it's supposed to be 1/3 cause probability is stupid but if you are going to guarantee that one is heads yer left with only one coin flip that has only 2 faces so 1/2. This is a case where theory is important for understanding a subject but reality is not the same. HH is a 1/3 probably in a 2 coin flip. Once you guarantee the result of one of the coins it's a one coin flip in reality as far as anyone not a cunt is concerned.
>>
>>703065799
it proves that you have no experience when working with sets, a really fucking basic aspect of logic

{a, b} = {b, a} and so does {H, T} = {T, H} and saying that the possible outcomes are { {H, T}, {T, H}, {H, H} } is fucking idiotic because youre basically saying that the possible outcomes are {a, a, b}
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>>703065732
>You are fucking told at least one landed heads.

Yes. In English, that could possibly mean that the value of one of the coins was ascertained.

>as you have no idea which coin landed heads

The wording of the problem leaves this vague. It could rationally be interpreted to mean that one of the coins' values was ascertained, while the other was in mid-air. "At least one was heads" matches the description of one coin landing on heads, and one coin being in a state of uncertainty. The wording is shit, no matter how you look at it.

>No, it's not. It's a basic conditional probability question, you fucktard. Only retards get confused because they don't understand probability. This is the basic layout of a conditional probability question:

It's one of two basic conditional probability questions, which produce mutually exclusive results. That's why it's a fun little meme to post, because its vague description reliable gets people to rationally interpret it either way. There's no confusion here, except perhaps yours. We understand the one way to look at the problem (one coin's value is ascertained, while the other is uncertain) and the other way to look at the problem (both coin's values are uncertain, yet results with double tails are excluded.)

>OP's question is
OP's question is if there are two binary states, and at least one of the binary states is 0, then what are all the remaining possible binary states?

The statement "at least one of the binary states is 0" is vague, because it could mean that one of the binary states is definitely 0, and one of them is 1 or 0, and that would certainly match the description of that sentence. Or, it could mean that both binary states are 1 or 0, but not both of them are 0.

But it doesn't "not both of them are tails" It COULD have. It would be rational for that to be the case. It makes one wonder how the problem should be worded if they intentionally wanted to ask for the version of the problem with a 1/2 probability/
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>>703062403
1/2

independent events.

If you got this wrong, you have nigger-tier intelligence.
>>
ITT idiots

The set of possible outcomes is {HH, HT, TH} which would lead you to believe that the probability is 33%.

However that is not what the probability is. The probability is the likelihood of achieving a HH scenario, which will be 50% across all flips.

Why is this?

Because the {HT, TH} set can only account for 50% of the flips as a whole. The only difference you would determine when tabulating data is which HT or TH will have the largest amount of the 50% (ie. 30% HT + 20% TH)
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>>703066366
( {a, b} = {b, a} ) =/= ( {HT} = {HT} )
This is so simple to see, and yet you're claiming others are inexperienced with sets.
>>
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>>703066330
This guy gets it.

You jackoffs going "NO IT'S NOT THIS WAY, IT'S ONLY THIS WAY" are still one level of retardation below the ultimate truth, which is that when encountering vaguely worded problems, that in itself becomes a special kind of probability problem, within a probability problem, because you then have to solve the probabilities for both plausible wordings of the problem.

It's a meta probability problem. That's the joke here, and why this is a popular meme.
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>>703062561
>2 coins
>independent events
>we know the value of one coin
>only thing remaining is the probability of the other event
>because INDEPENDENT EVENTS, you nigger
>P(H) = 1/2
>because only one coin matters
>you
>nigger
>>
>>703063037
Learn some set theory first. It's an ordered pair, so order DOES matter.
>>
First Coin: T, -> Second has to be H

First Coin: H, -> Could be H or T.
Meaning that both the first coin (50% chance with two possible outcomes you fucking idiots) and the second coin in the 1H system (50% chance with two possible outcomes you fucking idiots) both have the same chance of failing and getting T.

If you say 1/3, it's because you're a fucking idiot and think coins have three sides.
>>
>>703066277
Debate is over guise
>>
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Can I spend the coins?
>>
you guys are stupid, % of chances don't mean anything, you could flip those two coins and get HH 9 times out of 10 and you would say the outcome is 90%
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>>703066052
Lol
>>
>>703063073
>this isn't the monty hall problem
>the events are independent
>in monty hall you know what the first door contains, so probability is additive
>here EITHER could be heads
>ergo independent events
>ergo multiplicative probability
>ergo 1/2
>you're a dumb nigger
>>
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>>703066300

Holy fuck, you're retarded/

Try to follow along now. I'll attempt to explain this as easily as possible so even retards get it.

When you flip 2 coins, there are 4 equally probable outcomes likely. These outcomes and their probabilities are:

HH = 1/4
HT = 1/4
TH = 1/4
TT = 1/4

Now we are told that at least 1 coin landed heads, so only the TT outcomes does not satisfy the CONDITION in this CONDITIONAL probability question.

We are left with

HH = 1/3
HT = 1/3
TH = 1/3

or

HH = 1/3
HT/TH = 2/3

Do you understand now?

1/3

>Are you suggesting that a coin has a 1/3 chance of being heads even though there's only two sides?

No, you fucking simpleton. I am telling you that the probability that BOTH coins landed heads GIVEN that at least 1 coin landed heads is 1/3.

Try to keep up.

Here's a Venn diagram and Bayes' theorem solution for people who aren't morons.

1/3
>>
Pleasantly surprised to see so many getting it right. (1/3)

For those who are confused, I highly suggest reading up about the Monty Hall problem.
>>
>>703066599
Depends how the simulation was programmed.

That's one way to interpret the English of the original question into Turing code. There's also another plausible way to interpret the English of the original question into Turing code, which the programmer of that simulation failed to take note of.
>>
>>703066521
you're listing HT and TH as variables in the result set again... which makes the first half of your post {ab} = {ba}

put those comas back son,
>>
>>703066578
Actually, you flip them together, therefore you have just one event.
>>
>>703066300
One head is guaranteed, if you get one head, one third is already done. The other two thirds depends on the other coin. So while the options are only HT or HH, it's still a one third chance.
>>
>>703066330
Sorry 1/4 prob in a 2 coin flip. The idea for 1/3 here is yer not guaranteed which coon will land H so HT and TH while similar results aren't the same coin and therfore are 2 of the 3 options. HH is 1/3. But I Disagree Cause I'm STUBORN And Hate Yer bulshit. To guarantee one will land head and TT isn't an option you'd need one of the coins to be double H otherwise your just manipulating the odds of two regular coins flipping where HH is a 1/4 prob by removing from the data set all TT results Witch isn't gona happen with 2 real 2 faced coins.
>>
>given at least one is heads

This is NOT an ordered-pair problem. This is NOT the monty-hall problem, you *stupid* *fucking* *pretentious* *niggers*.
>>
>>703066710
Elaborate

The original question seems pretty straightforward to me
>>
>>703066330
>I kow it's supposed to be 1/3 cause probability is stupid
>math is stupid

I'll take a large fries with that, thanks.

>HH is a 1/3 probably in a 2 coin flip.

No it isn't, you fucking retard. it is a 1/4 probability.

HH = 1/4
HT = 1/4
TH = 1/4
TT = 1/4

At least 1 landed heads, so you now have

HH = 1/3
HT = 1/3
TH = 1/3

1/3
>>
>>703062403
.5 nigger
>>
>>703066700
>ugh yeah like coins have a 1/3 chance of landing on a side

Literally being this retarded

>Thinking that HT and TH are somehow different when you have the condition that ONE HAS TO BE H AND IT DOESNT MATTER WHICH ONE IS

It's okay, breathing and typing are hard to do at the same time for people like you
>>
>>703066816
>two regular coins WERE FLIPPED

You absolutely cannot infer that from the wording. If they're flipped at the same time, they're still independent events.

You are a stupid nigger.
>>
If you ask me, the answer to the question is 5/12.

There's a 50% chance it means the version of the problem where the correct answer is 1/2. There's a 50% chance it means the version of the problem where the correct answer is 1/3. Without the possibility of consulting the author of the probability, and no priors to build a Bayesian net from, the only rational thing to do here is to sum both probability sets, and take their average. 1/2+1/3=5/12.

The answer is 5/12, and everyone in this thread is not wrong, but less correct than this solution.
>>
>>703066879
See
>>703066860
I just type to slow to correct before you noticed. Hurray phone.
>>
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>>703066368

You're wrong and Washington University Math Dept. agrees.

It's a basic conditional probability question. It is clear and concise.

If the FIRST coin landed heads, the answer is 1/2

If AT LEAST ONE coin landed heads, the answer is 1/3

Source:
http://courses.cs.washington.edu/courses/cse312/11wi/slides/04cprob.pdf

Answer is 1/3 to OP question
>>
>>703066978
I liek you.
>>
>>703066578
Yeah but we don't know which coin we know the value of.

Therefore the possible outcomes are:
Heads/Tails
Tails/Heads
Heads/Heads

1/3
>>
>>703066449

You have nigger-tier intelligence. Don't ever gamble.

the answer is 1/3
>>
>>703067146
Yeah he might go around saying a coin has a 1/3 chance of being H because another coin already is.
>>
>>703066477
>Because the {HT, TH} set can only account for 50% of the flips as a whole.

You are twice as likely to get HT/TH as you are to get HH for a 2 coin flip, you moron

HH = 1/4
HT/TH = 1/2
TT = 1/4

Answer to OP = 1/3
>>
>>703066277
your code is wrong - you allow to increment bothheads and atleastoneheads in the same trial


also, according to your simulation, TT came up 0 times

solution: subtract atleastoneheads from bothheads. its MAGICALLY 50% you stupid nigger
>>
>>703062496
HOLY FUCK
>>
Yeah, it's 1/3. The fact that one of the coins is H means that it changes the probability of another independent event, right? And now that we know one is H, it means the chances of the coin falling H changes and is 1/3.
>>
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>>703066584
>If you say 1/3, it's because you're a fucking idiot and think coins have three sides

No, retard, it's because for a 2 coin flip where there is at least 1 heads, there are 3 equally likely outcomes.

heads, tails
tails, heads
both heads

1/3

If you disagree, answer this question in pic related
>>
>>703066876
Let's evaluate on the sentence "at least one of the coins lands on heads."

Here is one of the two possible probability outcomes for that wording:
>Two independent events, where one of the four outcomes is disregarded.

Here is the second of two possible probability outcomes for that wording:
>A single independent event, where one of the outcomes was ascertained.

Both of these probability outcomes satisfy the condition "at least one of the coins lands on heads."

The probability outcome where there are 0 independent events, because they both land on heads is disregarded, since that adds unnecessary specification to the condition "at least one heads." The probability outcome where there are 0 independent events is therefor an invalid interpretation of the wording.

The sentence "at least one of the coins lands on heads" does not sufficiently specify only one possible probability outcome, given that information alone.
>>
>>703067362
50%, because its either mixed, or both heads

mixed doesnt account for more than 50% just because there can be two different versions of mixed.
>>
>>703067110
Again I understand the theory but disagree. To assume one will be heads is to assume one coin is the same on both sides thus the only results possible are HH,HT thus 1/2. Otherwise 2 flipped 2 faced coins can be HH,HT,TH,TT thus 1/4. It's a nifty thought excersize to pretend TT isn't an option but this is where probability becomes more like philosophy than math and thus utter bullshit.
>>
>>703066978
i like this answer
>>
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>>703066876
>>703066710

>Turing Code

Ignore this fucking retard. It's a simulation written in C++.

Here's a Python implementation.

Also confirms 1/3
>>
0%. Both coins in the picture are tails.
>>
>>703067362
It's still 1/2.

The first coin has a 50% chance of being T, or H.
S1: C1 = T, meaning the next one HAS TO BE HEADS
S2: C1 = H, meaning the next coin can be EITHER HEADS OR TAILS (with a 50% chance)

How are you not getting this? Are you trolling?

In the first scenario, no other coin is tossed because we know it can't be T. (Meaning the first flip is the only one that matters, so it's 50%)
In the second scenario, we still understand (those of us with very basic math understanding, unlike you apparently) that a previous flip does not magically change the outcome probability for the next. (Meaning that it's also 50%, because coins have two sides as I'm guessing you're starting to gather.)

Simple stuff.
>>
>>703066277
if (atLeastOneHeads + bothHeads) > trials {
ImaHugeRetard = TRUE
}

you get more results than you do trials. Test your code before you rek yourself
>>
>>703066932
>>ugh yeah like coins have a 1/3 chance of landing on a side

Nobody said that, you fucking troll. Fuck off.

>HT and TH are the same
>penny=heads, quarter=tails
>is same as
>penny=tails, quarter=heads

You're not trolling anyone, retard.

1/3
>>
>>703067623
no they're talking about how to implement the statement in generic machine language. the point is, are you asking the machine to pre-set one coin to heads and then flip another ; or flip two coins and: check to see if both were heads, or flip one coin, then another, then state that one was heads, then find the probability that you keep getting that output ; or give an output every time a coin is declared heads.....

its actually a really cool meme if you appreciate the problems with the wording
>>
>>703066973
>If they're flipped at the same time

They can be flipped simultaneously, sequentially or a single coin could be flipped twice.

In all cases where at least one coin(or flip) landed heads, you will get both heads 1/3 of the time

1/3
>>
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>>703067110
Well. What can I say? WSU is incorrect.

If "the first flip lands on heads" then "at least one of the two flips landed on heads."

Hence if the value of the statement "at least one of the two flips landed on heads" is true, then it is possible that the statement "the first flip lands on heads" is either true of false, as per the definition of an if-then statement in stoic logic.

I am not a stranger to the educational system.

If that's from professor or something, I can help you write a formal argument that they can take to whoever teaches stoic logic at WSU.
>>
The chances are 100% just like my dubs here ^
>>
>>703067623
Turing code is applied at the machine code level. There is no way to run a simulation on C++ without invoking Turing code.

That Python implementation is not incorrect, but it is incomplete.
>>
>>703067845
>ur a troll therefore im right

Yeah, fitting in with the rest of the retard 1/3ers
>>
>>703067240
Do you know the meaning of the expression 'at least'? What a fucking retarded nigger
>>
>>703062403

How many chances that it falls standing up?
>>
>>703067492
>To assume one will be heads is to assume one coin is the same on both sides

You fucking retard.

1. REGULAR coins were flipped, not trick coins, not a double heads coin.

2. No coin WILL BE heads. AT LEAST one coin out of two LANDED heads.

Man, you can't even English.

>It's a nifty thought excersize to pretend TT isn't an option

Jesus Christ, please tell me you're trolling. Nigger, TT can NO LONGER be an option in the event that AT LEAST ONE coin landed heads.

You can have

heads, tails
or
tails, heads
or
heads, heads

1/3

>basic conditional probability
>more like philosophy

Jesus Christ
>>
>>703066277
But ~75 - ~25 = ~50

So 50% aka 1/2
>>
>>703068035
>but it is incomplete.

Just because you say so doesn't make it true.

Explain how it is incomplete so we can all laugh at you.
>>
>>703062561
fucking idiot. its 1/4
learn how to math
>>
This is getting pretty sad. If we know one is H, we only throw one coin.
50/50 chance for heads or tails, assuming both outcomes are equally probably
>>
>>703067132
nope

heads/tails
tails/heads
heads/heads
tails/tails

1/4
>>
>>703062403
>Two regular coins were flipped.
Four results: HH, HT, TH, TT.

>At least one landed heads.
Three results: HH, HT, TH. TT is forbidden.

What's the probability both landed heads?
1/3.

For people who disagree: try it with two coins.
>>
>>703067882
>the point is, are you asking the machine to pre-set one coin to heads and then flip another

No, you can fucking read the code. Each coinFlip() function generates a pseudo-random number (0 or 1), each with a 50% likelihood of occurring, representing heads and tails.

>basic conditional probability
>a really cool meme

These are the typed of faggots on /b/ nowadays.

1/3
>>
>>703068139
your code increments both values when they come up both heads, so actually you dont understand it

it first checks if at least one is heads and increments atleastone
but then instead of exiting the loop it goes on to check for bothheads in the same trial and may increment that as well

your code is shit
>>
>>703067474
Well I see your point. The fact that it says two regular coins is what I think makes me say it's 1/3
>>
>>703068424
Got TT. Therefore theory is invalid.
>>
>>703067712

I think I can see how you are retarded.

Answer this question to confirm my suspicions:

2 regular coins are flipped. What is the probability that both land tails?
>>
1/5 is the answer.
>>
50%.
>>
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this entire thread is a bunch of faggots who have shit for brains and maybe two people who took stats
>>
>>703068424
i can read the code, but it can be programmed differently based on a different interpretation of the original statement in the picture

reread it a few times and see some alternate interpretations
>>
>>703068432
It ain't my code.

Anyway there are 3 possible outcomes to each trial:
>Both tails - - > you don't count it
>Tail and head - - > you count one for 'at least one head'
>Both heads - - >you count one for 'at least one head' and one for 'both heads'

Even a 5 yo could understand this
>>
>>703067787

Both heads is a subset of at least one heads, you fucking retard.

Jesus Christ, /b/.

In other words, Both heads is counted in Atleast one heads, not separately you fucktard.
>>
>>703068271
Here, I basically covered the necessary points in these two posts. If that doesn't sufficiently explain, tell me what I'm missing from your point of view, and I'll cover that part again.

>>703067474
>>703067931
>>
>>703068047

Fitting in with Washington University Math Dept, faggot

1/3
>>
>>703068395
tails/tails is guaranteed to not happen faggot
>>
Take two coins, assume one is H. Doesn't matter if you put it down first or second.

Take the other coin and flip. What are the chances you'll get T instead of H on the coin that is not 100% H?
>>
>>703066578
this.

it doesn't fucking matter if you flip them together or separately, you already know one is GUARANTEED TO BE HEADS

it's 50%, and anyone who thinks otherwise is legitimately autistic
>>
>>703067931
>>703068770


WSU is not incorrect, but I will take on board your logic table and get back to you with an explanation.

Give me a few minutes.
>>
>>703066687
Hey nigger, the events are independent but there is a 100 prevent chance one lands on heads, so you only have to account for one coin landing on heads. Read the whole fucking problem next time.
>>
>>703069030
The thing is you don't know WHICH one is going to be heads
>>
>>703068537
1/4

Because you aren't given an H, every possible outcome is valid.
Because in the OP question you are given one H, only two outcomes are valid: 1) HH, and 2), NOT HH.
>>
>>703069181
it doesn't fucking matter WHICH one it's gonna be

the question does not care about coin sequence order.
>>
>>703068202
Not trolling if you flip 2 coins either TT is a possibility and HH is 1/4 or one is heads and the other Is 1/2. Otherwise your just ignoring 1/4 of the data to get the 1/3 result you want because muh data selection bias. My argument is that TT being an impossible result is an impossible situation unless one coin is H on both sides therfore HH,HT are the only posible outcomes. If both coins have H and T than possible results are HH,HT,TH,TT and HH is 1/4. HT,TH,TT is a fictional result set that cannot exist in reality with 2 real 2 sided coins.
>>
>>703069182
>being this retarded

If you flip 4 coins there are only 2 possible outcomes, HHHH and not HHHH
>>
>>703069303
If TT, then flip again.

Recursion.
>>
>>703068406
And TT will happen 1/4 the time. You cannot just forbidden reality.
>>
>>703068736
your code is flawed, you increment both values when both coins come up 1

just sum your results, they dont even add up!

75006885 + 24998912 = 100005797

you cant explain that, because you dont know what your code even does
>>
>>703067240
>you allow to increment bothheads and atleastoneheads in the same trial

Yeah, of course, dumbass. If you get both heads, then obviously you increment the bothHeads counter. And as bothHeads also contains AT LEAST ONE heads, you must also increment the at LeastOneHeads counter.

>also, according to your simulation, TT came up 0 times

No, retard, TT came up ~ 25% of trials, but counting TT is not necessary to get the probability of both heads given at least one heads.

See Bayes' theorem

What is probability of event A given event B?

A = "both coins are heads" = {(HH)} = 1/4
B = "at least one coin is heads" = {(HH), (HT), (TH)} = 3/4

P(A|B) = P(A∩B)/(P(B)) = (1/4)/(3/4) = 1/3
>>
>>703068997
>given that at least one of them landed heads
>at least one
>at least
You assume ONE of them is heads, not AT LEAST one.
>>
>>703069452
Read the OP pic, faggot.

It says "given that at least one of them landed heads."

Wanna try again, retard?
>>
>>703069373
>de river in egupt
>>
>>703067300
>The fact that one of the coins is H means that it changes the probability of another independent event, right?

No, you are confused. That's not what's happening here. That's not why the answer is 1/3.

>And now that we know one is H, it means the chances of the coin falling H changes and is 1/3.

No. At least one coin out of 2 landed heads. Neither coin influences the other.

When 2 coins are flipped, there are 3 equally probable ways to get at least 1 heads coin

heads, tails
tails, heads
heads, heads

heads, heads is 1 of those 3

1/3
>>
>>703067483
>because its either mixed, or both heads

It's TWICE as likely to be "mixed"

1/3 vs 2/3

Answer HH is 1/3
>>
>>703069400
>And TT will happen 1/4 the time. You cannot just forbidden reality.
You can discard results when they don't fit the ones you need (the ones with 1+ head[s]).
>>
>>703069182
>1/4

Holy shit, you got it correct. Okay so if the outcome is NOT both tails, what are the other possible outcomes and their probabilities?
>>
>>703069775
>Discard results cause they don't fit hypothesis.

Solid science.
>>
>>703069438
your probability for B is wrong because you list HT and TH as separate probabilities
(1/4)/(2/4) = 50%
>>
>>703069408
>you increment both values when both coins come up 1

That is CORRECT, you fucking retard.

>75006885 + 24998912 = 100005797

You fucking moron, the 24998912 is CONTAINED within the 75006885

You do not count them separately.

JESUS

I hope you are trolling.

1/3
>>
>>703069670
Except we know that if we get a T, the next one has to be H.
And if we assume that in that system, there's no need to throw a second coin (because we're ruling out the possibility of TT) then we have to also assume that if we flip an H, we have to place the same other coin down as a constant H.

If you don't want to do that, you either have to A) accept the possibility of TT and flip the second coin
or B) reword the question to allow different rules in different events (one flip for TH outcome and two for HH or HT outcomes)
>>
>>703069030
>anyone who thinks otherwise is legitimately autistic

No, anyone who understand the answer is 1/3 has some experience with conditional probability.

Conditional probability is counter-intuitive and that's the reason you get retards answering 50%.

The answer is 1/3

Flip 2 coins. At least 1 is heads. Could be

heads, tails
or
tails, heads
or
both heads

1/3
>>
>>703069975
Binary.

0 = 00 = TT
1 = 01 = TH
2 = 10 = HT
3 = 11 = HH

Are you claiming that 1 = 2?

If HT, and TH counted as the same probability event in binomial expansions, then the normal distribution wouldn't be a binomial expansion with as the exponent approaches infinity. But... it sure likes like it does from a graphical standpoint.
>>
>>703069438
>And as bothHeads also contains AT LEAST ONE heads, you must also increment the at LeastOneHeads counter.

you increment two results for one trial, intentionally? and you work with these results to get your final probability? what are you even doing...
>>
>>703062403
1H must be present, so we are left with 3 outcomes.

HH
HT
TH

we are interested in HH thats 1/3
HT and TH are not the same
>>
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Nobody is factoring in the variable of the chance the coins have to land on their side. smh
>>
>>703069933
Poor science but fine statistics - if it doesn't fit the premises assumed to be true (such as "at least one is heads"), you discard it.
>>
>>703069303

Do you know what CONDITIONAL probability is?

The condition is that "at least one coin landed heads." This means that from this point forward, TT is not a possible outcome.

Flip 2 coins. What is the probability that both land heads?

Answer = 1/4

FLip 2 coins. What is the probability that both coins landed heads given the condition that at least one coin landed heads?

Answer = 1/3
>>
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>>703062403
Every smartfag knows that ANY additional info reduces the Result Space so changes the odds away from the knee-jerk redneck toothless hillbilly 'obveeeus commmon sence' answer.

So it not be 1/2... dagnabbit.
>>
>>703070361
yes.
1 = {H, T}
2 = {T, H}
1 = 2

2 is just not ordered correctly
>>
>>703069054
The easier way to phrase my stance is:

Prove that "at least one of the two flips lands on heads" implies that it is not true that "the first flip lands on heads."

If ya' can't, then maybe the first flip *does* land on heads.
>>
>>703069623
And you assume one of them is heads, not at least one, ergo, you didn't read OP pic, faggot.
Wanna try again, retard?
>>
>>703069975
>because you list HT and TH as separate probabilities

That's because they are distinct, separate and equally probable outcomes, you simpleton.
>>
>>703062796
Fuck you are stupid
>>
>>703070724
no, they are the same outcome. one came up heads and the other came up tails

the order is irrelevant
>>
>>703070205
>Except we know that if we get a T, the next one has to be H.

Okay nigger.

Flip 2 coins, at least 1 landed heads, so could be

first coin = tails, second = heads
or
first coin = heads, second = tails
or
both coins = heads

those are the only 3 options/ All 3 of them are equally likely to occur.

1/3
>>
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>>703070309
heads, tails
and
tails, heads

is.
the.
SAAAMEEE FUCKING THIIIINNNGGG
>>
>>703064417
How long did it take you to make that up? Give up.
>>
>>703070633
Well, then either normal distribution is a flat line, or it's not the binomial expansion set, as its exponent approaches infinity.

Do you wanna' edit the wikipedia entry on that? Here it is, if you do.

https://en.wikipedia.org/wiki/Normal_distribution#Central_limit_theorem
>>
>>703070900
>being this retarded
>>
>>703070386

Fuck off you troll. Nobody can be this retarded.
>>
>>703062854
Look at the question
>2 coins are flipped. One of them will land heads
It does say which coin will land heads. Which means it's possible that the first coin lands tails and the second lands heads.
This means there is a difference between HT and TH.
>>
First, what kind of regularity are we talking about?
>>
>>703070647

At least one coin landed heads

does not imply that

the first coin landed heads.
>>
>>703062403
around 95%
>>
>>703071171
each node has the same degree
>>
>>703062403
>Two coins
>were flipped
>both landed heads
>At least one
>Both
>Landed
>Heads

the answer is 100%
>>
>>703070900
>no, they are the same outcome

Kill yourself.

Or read this and correct your retardation >>703063184
>>
So many retards here, one coin is guaranteed to land on heads according to OPs picture, the second is 50/50
Heads or tails .

HT or HH

2 options not 3 fuck
>>
>>703070931

>being this retarded

How do you manage it?
>>
>>703070569
I know what it is. I just have a deep philosophical disagreement with it. You're either flipping two coins or not. I wouldn't gamble at a casino where blackjack of Jclubs Aclubs was discarded and I rejected a reality where 2 2 faced coins flipped have a 1/3 Chance of HH.
>>
'bout three fiddy (fifty actually)
>>
>>703071338

first could be tails, second heads

3 options, all equally probable.

>HT or HH
or TH

1/3
>>
https://ideone.com/QzWjYI
don't mind me, just watching the thread burn
>it's 1/3 tho
>>
>>703071325
I already did, and I fixed it as the first quote
>>
>>703071457
>I rejected a reality where 2 2 faced coins flipped have a 1/3 Chance of HH.

But they HAVE a 1/3 probability of being HH GIVEN that at least 1 landed heads.

holy shit, anon.
>>
ITT: I'm so open minded that I belive all the bullshit my professor tells me. Hey guys if you flip 2 coins HH is 1/3 he said so and I sucked his dick so fuck you.
>>
I agree. Also,

At least one coin landed heads

does not imply that

it is not true that the first coin landed heads
>>
>>703071540
Yes there are three probabilitys but it's still 50-50.

HT TH HH
but that didn't answer OP question .
The question is what is the chance that one will land on heads if the other is already heads.

50%!

Unless the undecided coin lands on it's fucking side then it would make it 2/3.
>>
>>703071705
But you can't just decide one is going to be heads if you flip 2 coins. This is where we disagree. If you actually fucking flip 2 coins HH is 1/4. Even if you don't write down the TT results and flip again you've had to flip the coins again. This is why statistics is utter bullshit.
>>
>>703072030
Your answering a complete different question .
>>
>>703062403
HT and TH are indistinguishable since the coins are identical so its still 50/50
>>
>>703062403
The fuck is a 'smart'
>>
>>703071567
/thread
>>
Okay, let's break this down since no one reads anything.

"Two regular coins were flipped. What is the probability that both landed heads given that at least one of them landed heads?"

1. Two coins were flipped.
>The coins have already been flipped.
2. What is the probability that both landed heads given...
>After they have already been flipped, we are presented with two coins that have landed heads.
3. ...that at least one of them landed heads?
>Only one needs to be heads.

What we know now is that:
>Two coins were flipped
>Two coins both landed on heads
>The two coins are in the picture, landed on heads
>The probability of at least one of those heads being heads is 100%

The answer is 100%
>>
HH - 0.25
HT - 0.25
TH - 0.25
TT - 0.25

If TH = HT then

HH - 0.25
HT* - 0.5
TT - 0.25

Therefore HT still has twice the chance of happening as HH regardless of whether or not the coins are indistinguishable.

1 / (1+2) = 1/3
>>
>>703072002
>The question is what is the chance that one will land on heads if the other is already heads.

No, it isn't.

Read the question again.
>>
>>703072680
That was cute.

Thanks for that.
>>
just did a bunch of coinflips on random.org

the results came in 20 - 21 and then i stopped flipping because its obviously 50%

Try the same
>>
>>703062403

50%

The previous coin's result has no impact on the chance of the second coin you retards.
>>
>>703072030
>But you can't just decide one is going to be heads if you flip 2 coins.
>one is going to be
>going to be

Anon, 2 coins were flipped and at least one landed heads. Got it, now?

>If you actually fucking flip 2 coins HH is 1/4

Yes, without any conditions. But OP question is a conditional probability question. The condition is that "at least one coin landed heads." THEN you are asked for the probability that both are heads.

>This is why statistics is utter bullshit.

This is probability. Probability is solid math, anon.

1/3

>>703072228
>HT and TH are indistinguishable since the coins are identical so its still 50/50

Holy shit, you're retarded. You really think that using non-identical coins changes the probabilities?

>>703072750

Correct.

1/3
>>
>>703072978
How do you know there was a previous coin? How do you know they didn't land simultaneously?
>>
It's not 1/3 or 50% guys.

Look at each coin individually. In a 2 coin situation each of them has 2 results where that coin is heads, and two results where that coin is tails.

If you dismiss (TT) and leave
HH
HT
TH

Look at that for a second
H
H
T

H
T
H

That's a 66% chance for each coin to roll heads now. You guys fucked the entire equation by forcibly removing a result.

If one coin is heads there's a 66% chance the other coin is heads.
>>
>>703073083
If you're going to do it that way, you need to average the results, not add them.

If you did it with four coins, you'd quickly see that your probability exceeds 100%.
>>
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>>703073189
>>
>>703073189
Actually nevermind, I think I was putting subtext into your post that wasn't actually there.

>>703073083
The question asks what is the probability of both showing heads, not what is the average number of heads over time.

That's why you're double counting.
>>
>>703072978
>previous coin's result has no impact on the chance of the second coin

We know. The answer is still 1/3.

Flip 2 coins. 4 possible outcomes, all equally likely

HH
HT
TH
TT

3 out of those 4 contain at least 1 heads

HH
HT
TT

1 of those 3 is HH

1/3
>>
>>703073083

This faggot is trolling.
>>
>>703073482
Nah mate its 3/4
>>
>>703062403
99.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999% chance.
>very low chance that both land on my head
>>
>>703071119
Fuckin this.
>>
>>703071022
came here to post that aka babbys first stats class
>>
ITT: Retards think the answer is 50%
Thread replies: 252
Thread images: 32
Thread DB ID: 79561



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