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 solution
IMHO the probability you have evaluated is the probability of matching (same color) of 1st drawn with the last of same color.
No doubt - it is 1/3.
Therefore the probability of the opposite is 2/3.
I can therefore correctly a priori predict the color of the "last marble" drawn as being of opposite color to the 1st drawn with probability of 2/3.
Rem: This puzzle was not seen by me on the reviewing board (is there a by-pass lane?), otherwise I would have asked the author whether he wants a matching or a prediction.