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?

1/52.

Assuming no jokers, there are 52 cards in a deck at the start. When we transfer one from A to B, there are 53 cards in B and 51 cards in A. There is a 1/52 chance (case 1) that the transfered card is the king of hearts and a 51/52 (case 2) chance that it is not the king of hearts. In case 1, the odds of the king of hearts being on top of deck B is 2/53; in case 2, the odds are 1/53. So, overall, the odds are:

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

Posted by stan on 2004-02-05 08:30:09