How smart is Sup Forums?

How smart is Sup Forums?

Other urls found in this thread:

courses.cs.washington.edu/courses/cse312/11wi/slides/04cprob.pdf
youtube.com/watch?v=5Cqbf86jTro
twitter.com/NSFWRedditVideo

...

What coins?

25%

1/3.
Only autistic faggots would say 1/2..

The distribution of results will trend towards a probability of 50% for either binary result, with a large enough result set.

50/50 faggot

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

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.

And prior results do not influence future results.

Retards

P(two heads given one head) = P(two heads) / P(head for one coin) = 1/4 / (1/2) = 50%

2/3

TH = HT

why do i even bite?

Fucking this

Because HT and TH are two different possible results.

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 Sup Forums to be real life.

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

1/3 muthafucker.

You just went full retard

>TH = HT

You're fucking retarded.

You're retarded.

>thinking TH and HT are the same
It's ok to be wrong sometimes.

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.

its correct. result sets are equal if they contain the same items, the order is irrelevant

>tfw Sup Forums is smarter than you though
>tfw people are still confused by the Monty Hall problem

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

But it does make perfect logical sense. On of the solutions was KNOWINGLY removed, not randomly.

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.

Yeah, mb I was typing in a hurry on a phone, meant common sense

This unupset me, thanks user.

>mfw people actually think it's 1/2

Idiot.

33.3%

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

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.

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.

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.

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.

You're retarded.

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

1/3

>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

It depends how many times I was woken up, asked what day of the week it was, and put back to sleep.

youtube.com/watch?v=5Cqbf86jTro

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.

Every variable is a dimension, you tin can. Lrn2fucking analysis.

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

kek

Kill yourself.

>because one coin is always a head

Which coin?

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

>Which coin?
does it matter? you flip the first one. It's heads. you flip the second one, it's heads or tails.

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.

>you flip the first one. It's heads.

But that's not what happens, retard.

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?

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

Then you cover them and a person that can see them tells you that at least one of them is heads.

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.

1/3 tards
If you care read pic related

>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

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

>Thinking this proves you right

50% the probability for any variation and and number of flips Will always be 50%

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?

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...)

>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

Knowing that every Sup Forumstard has wasted their luck on repeating digits there is 0% chance for both coins to land head.

It says two coins, not two different looking coins you mouthbreathing autist.

I concer.

Third-ed

50%

source: math major

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.

>I'm a math tutor sometimes
>I rely on quantum mechanics

Kill yourself.

Refer to this, are you arguing with the author who has a PhD?

yes i am arguing

1/3

source: PhDs in Logic, Applied Mathematics, Analytics

It's 0% those are euros, no head on them

I feel like this is a bait but I'm all ears regardless since I'm a fucktard at maths

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

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%

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.

forgot to link

It's not mine, see Sheldon M. Ross

>before given
meant after

Simulation confirms 1/3

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

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.

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}

>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/

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)

( {a, b} = {b, a} ) =/= ( {HT} = {HT} )
This is so simple to see, and yet you're claiming others are inexperienced with sets.

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.

>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

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.

Debate is over guise

Can I spend the coins?