Question

A high school principal must select 14 girls at random from the freshman class to serve as hostesses at the junior-senior prom. There are 170 freshman girls, including 10 from minorities, and the principal would like at least one minority girl to have this honor. (Round your answers to two decimal places.)

(a) If he selects the girls at random, what is the probability that he will select exactly one minority girl?


(b) If he selects the girls at random, what is the probability that he will select no minority girls?


(c) If he selects the girls at random, what is the probability that he will select at least one minority girl?

Answer 1

Let X be the number of minority girls selected. Then

X ~ Binomial(14,1/17)

The probability distribution is given as follows:

X	P(X=x)
0	0.427952
1	0.374458
2	0.152123
3	0.038031
4	0.006537
5	0.000817
6	0.000077
7	0.000005
8	0.000000
9	0.000000
10	0.000000
11	0.000000
12	0.000000
13	0.000000
14	0.000000

(a)

P(Exactly one minority girl) = 0.37

(b)

P(No minority girls) = 0.43

(c)

P(atleast one minority girl) = 1 - P(no minority girl) = 1 - 0.43 = 0.57

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