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?

There is a 1/51 chance a King of Hearts was the card transferred to deck B, and drawing a King of Hearts in this case is 2/53.

There is a 50/51 chance a King of Hearts was not the card transferred to deck B, and drawing a King of Hearts in this case is 1/53.

The overall probability of drawing a King of Hearts is (1/51)*(2/53) + (50/51)*(1/53) = 52/2703

Posted by Brian Smith on 2004-02-05 09:09:12