A deck of 52 cards is shuffled and cut into two halves of 26 cards each. What is the probability that the number of red cards (hearts and diamonds) in the first half is equal to the number black cards (clubs and spades) in the second half?
Two jokers are added to the deck. The deck of 54 cards is shuffled and cut into two halves of 27 cards each. Now what is the probability that the number of red cards in the first half is equal to the number black cards in the second half?
Part 1. This is guaranteed. The probability is
1.
r=red cards in first half
26r=red cards in other half
r=black cards in other half
Part 2. There are two ways for the jokers to end up
a) The jokers end up in opposite halves. This guarantees the result.
The probability of this is 27/53.
b) The jokers end up in the same half. This makes the result impossible. The half with the jokers will have 1 fewer of each color than the opposing color in the other half.
So the total probability is 27/53.

Posted by Jer
on 20170605 09:29:12 