I toss two coins and look at the outcome.
I then tell you that at least one of the coins is showing up as "tails". What is the chance that the other one is showing "tails" as well?
(from techInterview.org)
(In reply to
re(2): Solution Using Real Prob/Stats by Eberhard)
HT and TH are "functionally equivalent" (as you put it) only if the function is "one coin is heads and one coin is tails".
If I flip two fair coins together a bunch of times, I will expect to get one of three outcomes:
(1) two heads, 1/4 of the time
(2) one head and one tail, 1/2 of the time, and
(3) two tails, 1/4 of the time
(I assume you agree with this so far.)
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The problem states:
"at least one of the coins is showing up as 'tails'."
This rules out outcome (1).
Outcomes (2) and (3) are still possible.
The probability of those two outcomes have a 1/2 : 1/4 ratio, and the question asked what is the chance the outcome is (3).
(1/4) / [ (1/2) + (1/4) ] = (1/4) / (3/4) = 1/3
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Please continue with your statistics class.
re(3): Solution Using Real Prob/Stats
