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Red vs Black Cuts (Posted on 2017-06-05) Difficulty: 3 of 5
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?

See The Solution Submitted by Brian Smith    
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Solution Another way of approaching it Comment 8 of 8 |
In a 27-card draw, the probability of not drawing a joker is (52/54) * (51/53) * (50/52) * . . . * (26/28)

Or [52!/25!] / [54!/27!]

Or (26 * 27) / (53 * 54) = 26/106

(26/106) * 2 ways to draw 27 = 26/53.

So the probability of drawing 1 is 1 - (26/53) = 27/53

  Posted by hoodat on 2017-06-12 13:27:03
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