Explanation Given: A standard deck of 52 cards. Approach: Expectation of a random variable x can be given by E ( x ) = ∑ x x p ( x ) . Calculation: Let x = number of aces . As, three cards are drawn, so, possible value of x can be as below. x = 0 , 1 , 2 , 3 Now, probability of getting no aces, that is, all the three drawn cards are non-aces. As there are 48 non-aces cards. So, p ( x = 0 ) = c 48 3 c 52 3 = 48 × 47 × 46 52 × 51 × 50 = 103776 132600 = 4324 5525 Similarly, probability of getting one ace, that is in three drawn cards two are non-aces. There are 4 aces and 48 non-aces cards in a deck of 52 cards. So, p ( x = 1 ) = c 4 1 × 48 c 2 52 c 3 = 1128 5525 In the same way probability of getting two aces and one non ace card is To determine (b) To find: The expected number of clubs when three cards are drawn from a standard deck of 52 cards.

2nd Edition

ISBN: 9780321964038

Author: GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher: Pearson Addison Wesley,

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Chapter 12.CR, Problem 91CR

To determine

(a)

To find:

The expected number of aces when three cards are drawn from a standard deck of 52 cards.

To determine

(b)

To find:

The expected number of clubs when three cards are drawn from a standard deck of 52 cards.

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Chapter 12.CR, Problem 90CR

Chapter 12.CR, Problem 92CR

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(a) To find: The expected number of aces when three cards are drawn from a standard deck of 52 cards.

Solution Summary: The author explains how the expected number of aces is 0.231 when three cards are drawn from the deck of 52 cards.