Two cards are drawn in succession from a deck of cards The f

Two cards are drawn in succession from a deck of cards. The first card is replaced and the deck is reshuffled before the second card is drawn. What is the probability that the two cards are (a) both kings, (b) an ace on the first draw and a king on the second draw, and (c) an ace and a king in either order?

Please show all work.

Solution

A.

There are 4 kings out of 52 = 1/13.

Hence,

P(both kings) = (1/13)(1/13) = 1/169 or 0.005917

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B.

The same way, there are 4 aces out of 52. Thus, drawing an ace is 1/13 in probability.

Hence,

P(ace then king) = (1/13)(1/13) = 1/169 = 0.005917

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C.

The first card can either be a king or an ace. It has 8 choices out of 52 = 2/13.

The second card only has 4 choices, as it is already restricted. Thus, second event is 4/52 = 1/13.

thus,

P(ace then king in either order) = 2/13 * 1/13 = 2/169 or 0.01183