An urn contains 5 black and 20 white marbles. They are to be drawn one at a time until all of one color has been exhausted.
What is the probability that the color of the first draw correctly predicts the first color exhausted?
(In reply to re: solution
by Ady TZIDON)
You say "IMHO the probability you have evaluated is the probability of matching (same color) of 1st drawn with the last of same color." (emphasis added)
However, I state, in the conditional probabilities, and therefore carrying over into the overall probability:
There is a 1/5 probability that the first drawn will be black. The conditional probability in this case is 20/24 that the last marble drawn will be white, which is the same as saying that the black marbles will be exhausted before the white.
and similarly for a first-drawn of white. That is, I've evaluated the probability of pairing (not matching) of 1st drawn with the last of opposite color, taking into consideration the reversal you mention.
We can see that the 20/24 is the probability that white will be the last if the first-drawn is black, and therefore that the black will be exhausted first, matching the black that had been drawn first, lowering black's count from 5 to 4.
Posted by Charlie
on 2015-08-12 08:42:24