Two identical pack of cards A and B are shuffled throughly. One card is picked from A and shuffled with B. The top card from pack A is turned up.
If this is the Queen of Hearts, what are the chances that the top card in B will be the King of Hearts?

(In reply to Solution by stan)

Given that the Queen of Hearts was turned up on the first deck, the card that was transferred to deck B is equally likely to be any one of the 51 other cards in the deck, so the probability is

(1/51)*(2/53)+(50/51)*(1/53)=52/(51*53)=52/2703

or about 0.0192378838327783943 rather than the 0.0192307692307692307 that 1/52 would be.

Posted by Charlie on 2004-02-05 08:43:55