The hardest brainteaser that you ever did see
I have 2 fair coins (its a recession after all).
I toss them both but you cannot see how they land.
I say "one of them is heads." - This is a true statement.
What is the probability that the other is heads?
Are the results independent of each other? i.e. does the result of the first coin affect the probability of the second coin?
And while we're on the subject, here's some more: Harder brainteaser than the coin flip, Trazer Mental Math Challenge and An even harder brain teaser "I'll one up Trazer"
Post answers, but keep reasoning out of the first few replies so people can try this for themselves.
OP edit: someone has posted a correct solution in the answers. Do NOT scroll down if you wish to attempt this fairly (none of the top few are right however).






I'm not a brainteasers guy,
I'm not a brainteasers guy, but theoretically isn't it 50/50 still
the probability of the event
the probability of the event that ONE coin is heads is 50/50.
the probability of the first coin being heads is 50/50.
the probability of the second coin being heads is also 50/50.
HOWEVER, the probability of the event that BOTH coins are heads is something else.
For any casual observers,
For any casual observers, still waiting on a correct solution.
.5
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The result from the first
The result from the first coin has nothing to do with the behavior of the second coin.
Newflyer wrote: The result
The result from the first coin has nothing to do with the behavior of the second coin.
This is not applicable to this question. Read it carefully.
1/3
1/3
1/4
1/4
one right so far.
one right so far.
1/4 this is a binomial random
1/4 this is a binomial random variable
P(1 Heads, 1 Tails) = .5 +
P(1 Heads, 1 Tails) = .5 + (.5 * .5) = .75
-- > = P(tails) + (P(tails)*(Pheads))
P(2 Heads) = .5 * .5 = .25
P(1 Heads after knowing 1 Heads) = .75 - .25 = .5
Depends on how you interpret
Depends on how you interpret the question:
You say one of them is heads and that this is a 'true statement'. This could mean ONLY one of them is heads or AT LEAST one of them is heads. If it's ONLY one then the probability that the other is heads is zero.
If it's at least one then there are three possibilities when at least one is heads: HT, TH, HH. The only possibility when the other one is also heads is HH, so the probability is 1/3.
he said 1 is heads and this
he said 1 is heads and this is a true statement, thus the second is not heads
1/3, this question's
1/3, this question's retardedly easy, most of WSO is retarded
The answer is clearly
The answer is clearly 1/3.
There are four, equally possible, outcomes from flipping two fair coins.
HH
HT
TH
TT
We assume that at least one coin is heads ruling out TT.
We now have 3 possible scenarios (HH, HT, TH) all of which are, again, equally possible. Of these three possibilities only HH has two heads (obviously) so the probability is 1/3.
XPJ wrote: P(1 Heads, 1
1/3 is correct. fascinating
This is assuming you look at
Work hard, play hard.
1/3 There are four outcomes
cond prob.
IlliniProgrammer wrote: This
Trazer, I hate to say it, but
Work hard, play hard.
Its 1/3, and the explanations
Just Do It
couchy wrote: cond
Just Do It
I understand everyone's
IlliniProgrammer
Really - most marble problems
Just Do It
Of course- once you see the
Work hard, play hard.
nyc123 wrote: I understand
I see the distinction now,
IlliniProgrammer wrote: Of
JoshFi7 wrote: nyc123
Just Do It
trazer985
Just Do It
nyc123 wrote: I understand
Work hard, play hard.
maximumlikelihood wrote: If
Work hard, play hard.
IlliniProgrammer
maximumlikelihood
notatrollatall
nyc123 wrote: I understand
Work hard, play hard.
Quote: ???? Please do go into
Work hard, play hard.
IlliniProgrammer
i did a monte carlo
This thread gave me a sad.
It depends how prestigious
YOU JUST GOT TROLLED
http://www.troll.me/images/red-foreman322/dont-you...
^ LOL
notatrollatall
how big are the coins? what
JoshFi7
I find this question really
nyc123 wrote: I find this