brando@linus.UUCP (Thom Brando) (08/19/83)
OK, I answered 1/2 to the probability of having chosen the double-gold
cabinet, but I think the following demonstrates, sans intuition, why
2/3 is the "correct" answer:
Let A represent the event that you have chosen a drawer containing a
gold coin, and let
B represent the event that you have chosen the double-gold cabinet.
Then the probability that you have chosen the double-gold cabinet,
given that you have chosen a drawer containing a gold coin, is
p(B|A) = p(BA) / p(A).
If you agree that p(A) = 3/6 = 1/2 and p(BA) = 1/3, then you should
also agree that p(B|A) = 2/3. I only wish I had taken the time to
think before I "guessed" 1/2 (after all, it IS intuitive, isn't it!).