Suppose that two cards are randomly selected from a standard 52-card deck. (a) W

Question

Suppose that two cards are randomly selected from a standard 52-card deck. (a) What is the probability that the first card is a spade and the second card is a spade if the sampling is done without replacement? (b) What is the probability that the first card is a spade and the second card is a spade if the sampling is done with replacement? (a) If the sampling is done without replacement, the probability that the first card is a spade and the second card is a spade is Round to three decimal places as needed.) (b) If the sampling is done with replacement, the probability that the first card is a spade and the second card is a spade is. (Round to three decimal places as needed.)

Explanation / Answer

There are 13 spade cards in single 52 card deck.

P( Card is spade) = 13 / 52

a)

P(first card is spade) = 13/52

Since second card is picked without replacing first, there are 51 total cards left with 12 spade cards.

P(Second card is spade) = 12 / 51

Therefore,

P( First card is spade and second card is spade) = 13 / 52 * 12 / 51

= 0.059

b)

Since second card is drawn with replacing first, probability to pick second card is same as probability to draw

first card.

P( First card is spade and second card is spade) = 13 / 52 * 13 / 52

= 0.063

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