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 Logical Test : Coinflip

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Shoop

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PostSubject: Logical Test : Coinflip   Fri Apr 13, 2012 9:34 pm

I flip 2 coins and you ask me if at least one of them is heads? I answer yes.

What is the chance that the other coin is heads aswell? (Given that you can trust my answer).
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e8lakes

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PostSubject: Re: Logical Test : Coinflip   Fri Apr 13, 2012 10:01 pm

P(A): First coin is heads.
P(B): Second coin is heads.
P(X): Chance that both coins are heads.

P(X) = P(A)*P(B)
P(A), P(B) = 1/2
P(X) = (1/2)^2 = 1/4

That's because there are 4 different pairs of possible results and only one is fitting the event we search:
h: heads
t: tails
(h, h), (h, t), (t, h), (t, t)


Since we can rely on P(A) being heads this does change:

P(X) = P(A)*P(B)
P(A) = 1
P(B) = 1/2
P(X) = 1*(1/2) = 1/2

That's because there are only 2 different pairs of possible results left and only one is fitting again:
h: heads
t: tails
(h, h), (h, t), (t, h), (t, t)


The chance for the second coins to be heads is 1/2.


Last edited by e8lakes on Fri Apr 13, 2012 10:04 pm; edited 1 time in total
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Effloresce

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PostSubject: Re: Logical Test : Coinflip   Fri Apr 13, 2012 10:04 pm

1/3 xD
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e8lakes

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PostSubject: Re: Logical Test : Coinflip   Fri Apr 13, 2012 10:25 pm

pfft oO

we only search for (h,h):

first heads is given: so there is only (h, t) and (h, h) left of what you can throw
the chance to get (h, h) instead of (h, t) is 1/2

you could also say that

P(A) = 1/4 --> {(h, h)}
P(B) = 1/2 --> {(h, h), (h, t)}

P(A|B) = (P(A & B)/P(B) = (0.25 & 0.5)/0.5 = 0.25/0.5 = (1/4)/(1/2) = (1*2)/(4*1) = 1/2
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EnStekPaNnaWOLF



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PostSubject: Re: Logical Test : Coinflip   Fri Apr 13, 2012 11:16 pm

There is 4 possible outcomes when you flip the coins.

(h,h) (h,t) (t,h) (t,t)

Given atleast one is heads we can remove (t,t). That leaves us with 3 alternatives, (h,h) (h,t) and (t,h). There is with other words 1/3 chance that it's (h,h).

My answer is 1/3.


Last edited by EnStekPaNnaWOLF on Sat Apr 14, 2012 1:49 pm; edited 2 times in total
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e8lakes

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PostSubject: Re: Logical Test : Coinflip   Fri Apr 13, 2012 11:18 pm

Shoop wrote:
I flip 2 coins and you ask me if at least one of them is heads? I answer yes.

What is the chance that the other coin is heads aswell? (Given that you can trust my answer).

Why do you all answer the blue part? Isn't the red part the actual question??
oh, he didnt say the first one is heads, just one.. OOpsie
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Night



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PostSubject: Re: Logical Test : Coinflip   Sat Apr 14, 2012 12:41 am

1/4
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XXXandBEER



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PostSubject: Re: Logical Test : Coinflip   Sat Apr 14, 2012 5:54 am

It does not matter if the previous coin was heads or tails. The odds are still 50 50 when you flip the new coin.
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BEeeH

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PostSubject: Re: Logical Test : Coinflip   Sat Apr 14, 2012 9:20 am

gewgwe


Last edited by BEeeH on Thu Jun 13, 2013 11:24 am; edited 1 time in total
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Chakra



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PostSubject: Re: Logical Test : Coinflip   Sat Apr 14, 2012 9:52 am

1/2
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BEeeH

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PostSubject: Re: Logical Test : Coinflip   Sat Apr 14, 2012 10:02 am

ghrehrereh


Last edited by BEeeH on Thu Jun 13, 2013 11:24 am; edited 5 times in total
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LAUCHISBACK



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PostSubject: Re: Logical Test : Coinflip   Sat Apr 14, 2012 10:03 am

wow geeks
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BEeeH

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PostSubject: Re: Logical Test : Coinflip   Sat Apr 14, 2012 10:55 am

gwegewweg


Last edited by BEeeH on Thu Jun 13, 2013 11:24 am; edited 1 time in total
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VsKatshuma

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PostSubject: Re: Logical Test : Coinflip   Sat Apr 14, 2012 11:32 am

It is obviously 1/3 chance.

Beeeh- is a turd.
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VsKatshuma

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PostSubject: Re: Logical Test : Coinflip   Sat Apr 14, 2012 11:45 am

Ok I didn't give it much thought at 1st and jumped to a conclusion. This is indeed an interesting problemz. Very Happy

It's almost like a trick question. The fact that the question already says "One is heads" means that the question is based on a situation where a Tails + Tails did NOT occur. In this case 1/3 is the right answer.

But it's not that simple. The 1/2 works if the two coin tosses are treated as independent events, but that would mean that the cointosser ignored all tosses where the 1st coin came out as tails.

I can somehow understand why the 1/2 makes sense but I still stand by 1/3 in this one.
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BEeeH

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PostSubject: Re: Logical Test : Coinflip   Sat Apr 14, 2012 12:03 pm

gwegwewe


Last edited by BEeeH on Thu Jun 13, 2013 11:25 am; edited 1 time in total
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VsKatshuma

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PostSubject: Re: Logical Test : Coinflip   Sat Apr 14, 2012 12:08 pm

OK I throw some Logix into this shit so that I got materials to reference to laters, if u 1/2 nubs still wana argue.

The question itself is a trick that creates an illusion for the separate coin tosses to be considered as individual events. By this logic, the other coin toss will ALWAYS be Heads, its like a trick where the coin tosser tosses the 1st coin over and over again until he gets Heads, then throws the other one. By this logic the question "I throw 2 coins. I say other one is Heads, what is the probability for the other one to be Heads too?" becomes "I throw 1 coin. What is the probability for it to be Heads?" instead. In this case the answer is obviously 50%, but IMO this is not how the question works.

If we consider the 2 coin tosses as separate events that have nothing to do with each other, the answer is 50%

If we consider the 2 coin tosses to be in the same pool, where we don't know the relation between coins, the answer is 1/3 (or 33,33...%)

The original question states that ONE of the coins is Heads. It's like the coins were thrown at the same time to the bottom of a coffee cup, so they get mixed and you can't classify the coins to a "first" and "second" one. In this case either one of the coins can be Heads. The third case is the case where both of them become Heads, ignoring all TT results, so the final probability becomes 1/3.

I am 99% sure that 1/3 is the right answer. The only argument that all 50%-dudes can use is the "It's a trick question, the 1st one is always Heads." As I said, IMHO this is not how the question is supposed to work. Beeeh- and bois are misdeducing the question. This brings me to the final verdict: The question itself can be approached from two different angles, yielding 2 different results. The correct answer depends on the setting of the question and the way of deducing it.

But still, 1/3 ftw ^^
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XXXandBEER



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PostSubject: Re: Logical Test : Coinflip   Sat Apr 14, 2012 12:27 pm

Throw one coin in the air its has TWO SIDES THERE FORE 50% chance its HEADS 50% chance its TAILS. 1/2

The fact there is another coin simply does not matter. These coins have no statistical knowledge of what its ancestor coins did. Coins are inanimate objects they have clue whats going on around them.
I can have 50 coins all heads land heads and still that 51st coin has a 50% chance of being heads.


On a side note who is VsKatshuma?
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BEeeH

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PostSubject: Re: Logical Test : Coinflip   Sat Apr 14, 2012 12:36 pm

gewsgew


Last edited by BEeeH on Thu Jun 13, 2013 11:25 am; edited 1 time in total
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mungo



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PostSubject: Re: Logical Test : Coinflip   Sat Apr 14, 2012 1:07 pm

rofl beeeh ftw Very Happy
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Effloresce

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PostSubject: Re: Logical Test : Coinflip   Sat Apr 14, 2012 5:45 pm

Quote :


If the original question was:
"You flip two coins. The first one came up heads. What are the chances that the second one is also heads?"

Then you would be correct to say 50%. But since the question was:
"You flip two coins. ONE OF THEM came up heads. What are the chances the second one is also heads?"

then the answer is 33%

Its an easy trap to fall into. Just because you've narrowed it down to two choices (both heads, or one heads and one tails), doesn't mean that those two choices are equally likely. In this case, they are not.

This is similar in some ways to the Monty Hall problem. You ultimately are faced with two choices, but those two choices actually have different odds.

Quote :

Once the event has occurred, the numerical distribution of the alternatives do not change. But, when information given occurrences, the relative distribution (a.k.a probability) DOES change.

100 flips -- HH 25 - HT 25 - TH 25 - TT 25

When the coins are flipped, the 4 alternatives -- HH, HT, TH, TT -- have an even distribution, and consequently each has a 25% probability.

But, information eliminates the TT alternative. So, for the purposes of calculating the probability of a remaining alternative, the 25 TT flips must be eliminated from consideration.

HH 25 - HT 25 - TH 25 -- 75 total flips
--> each alternative has 33% (25 / 75)
The HH alternative is what we are looking for, and it has 33% probability.

The question "the dime is heads, what is the probability that the penny is also heads" would have a 50% answer, because 2 of the 4 alternatives would be eliminated.

The question "what is the probability of both coins being heads" yields a 25% answer.



YEEEEEEEEEEEEEEeeeeeeeeeeeeeeeeeeeEEEEeeeeeeeeeeeeeeeeeeeeeeee


yo0oooooo000000000
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Shoop

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PostSubject: Re: Logical Test : Coinflip   Sun Apr 15, 2012 12:40 am

Aight kids its time for answer. And yeah many of you were right. It is ofcourse 1/3 chance.

Its pretty simple. As many of you explained, there are originally 4 different possibilities.

HH
HT
TH
TT

When you know at least one of the coins is heads, you can deduce its not TT, so you are left with :

HH
HT
TH

And in just 1 of these 3 cases is the other coin also heads. So 1/3. Well played, Sidey was first with answer and Stek was first with showing he understood the reasons behind the answer.
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VsKatshuma

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PostSubject: Re: Logical Test : Coinflip   Sun Apr 15, 2012 3:08 am

As usual Beeeh- sux

0 epicness
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Effloresce

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PostSubject: Re: Logical Test : Coinflip   Sun Apr 15, 2012 6:07 am

Geeks got TRASHED


WIZZA WIZZA WONG WANG baaaaaaaWEEEEEEZZZZZ
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CHIEFHERO[SKS]

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PostSubject: Re: Logical Test : Coinflip   Sun Apr 15, 2012 7:58 am

i agree with beer actually. its common knowledge that coins cant speak, so the first coin cant tell the second one what it landed on. they dont have a language. they also dont have eyes to see. so how can coin 2 know if coin 1 is tails or head? it cannot. it must be 50-50 chance.
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