A single card is drawn from a deck of cards What is the prob

A single card is drawn from a deck of cards. What is the probability that it will be (a) either a king or a face card, (b) either a king or a spade, and (c) either a heart or a face card?

Please show all work

Solution

A.

The \"king or face card\" are kings, queens, and jacks. There are 12 of them.

Thus, P(king or face card) = 12/52 = 3/13 [answer]

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B.

There are 4 kings, and 13 spades. However, 1 spade is a king.

Thus, there are 4 + 13 - 1 = 16 such cards.

Thus, P(king or spade) = 16/52 = 4/13 [ANSWER]

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There are 12 face cards, and 13 hearts. However, 3 face cards are hearts.

Thus, there are 12 + 13 - 3 = 22 such cards.

Thus, P(heart or face) = 22/52 = 11/26 [ANSWER]