Question

A deck of cards is shuffled and then divided into two halves of 26 cards each. A card is drawn from one of the halves; it turns out to be an ace. The ace is then placed in the second half-deck. The half is then shuffled, and a card is drawn from it. Compute the probability that this drawn card is an ace.

Answer 1

10/27.

Explanation:

The first half could have had, 1, 2, 3 or 4 aces in it.

If it had 1 ace then Prob( Ace on the second draw) = 4/27 or

If ... 2 aces .............................................................. = 3/27 or

If.............3 aces ............................................................... = 2/27 or

If..............4 aces ................................................................ = 1/27

Required probability = 1/27 + 2/27 + 3/27 + 4/27

= 10/27 answer.