Michigan State University - Diagnostic Exam

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5.18

  •   Suppose that in a school half of the students are boys and half are girls. Five students are selected at random. What is the probability that among five students selected at least four are girls?

    a) 5∕16 b) 1∕2 c) 3∕8 d) 3∕16 e) 5∕8

Solution:

P (≥ 4 H ) = P((exac)tly 4 H ) + P(exactly 5 H ) | 5 | ( )4 ( ) ( )5 = || 4 || 1- 1- + 1- ( ) 2 2 2 ( ) 1- 5 -3- = 5 2 = 16

Diagnostic:

If you miss this question please review Addition Principle.

Also, see 5.16: Counting (Permutations and Combinations) .

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July 15, 2008