A standard deck of cards is being used to play a game. There are four suits (hea

Question

A standard deck of cards is being used to play a game. There are four suits (hearts, diamonds, clubs, and spades), each having 13 faces (ace, 2, 3, 4, 5, 6, 7, 8, 9, 10 jack, queen, and king), making a total of 52 cards. This complete deck is thoroughly mixed, and you will receive the first 2 cards from the deck without replacement. Complete parts (a) through (d) a. What is the probability that both cards are spades? P(both spades)-0588 (Round to four decimal places as needed.) b. What is the probability that the first card is a 10 and the second card is a 5 or a 6? P(10 followed by 5 or 6)-(Round to four decimal places as needed.)

Explanation / Answer

a. Probability of first card being a spade = 13/52

Probability of second card also being a spade = 12/51

=> Probability that both cards are spades = 13/52 * 12/51 = 0.0588.

b. Probability that the first card is a 10 = 4/52

After the first draw, we have 51 cards with 4 5s and 4 6s, 8 in all.

Probability that the second card is a 5 or a 6 = 8/51

=> Probability of both events = 4/52 * 8/51 = 0.0121.

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