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?

We've all been duped, or should i say we've all duped ourselves, the chances of picking the king from back A is not 1/51, you select the 1st card from pack A before you know that the Queen of hearts was the top card, therefore the chances of seeing 2 king of Hearts in pack B is increased by 1/52 to (1/52)+1
this can then be divided by the total number of cards in pack B to give the following equation.

((1/52)+1)/53 = 0.01923076923076923

or 1/52.00000000000000208

Posted by Phil on 2004-02-06 13:45:34