Michigan State University - Diagnostic Exam

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5.11

  •   The probability that when two cards are drawn, without replacement, from a deck of 52 cards, that both are spades is which of the following?

    a)  1 1 ---⋅--- 52 51 b) 1 1 --⋅-- 4 3 c) 1 1 ---⋅--- 13 12 d) 4 3 ---⋅--- 13 12 e) 13 12 ---⋅ --- 52 51

Solution:

Let Sj denote the event “the jth card is a spade”. Then

P (S1 and S2) = P (S1)P (S2|S1) = 13-⋅ 12- 52 51

Diagnostic:

If you miss this question please review the definition of probability.

Also, see 5.9: Counting (Permutations and Combinations) and 5.14: Probability .

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July 15, 2008