Question

14. A jury pool consists of 27 people, 15 men and 12 women. Compute the probability that a randomly selected jury of 12 people is all male.

Answer 1

Given:

Total number of people (n)=27

men =15

women=12

$^{}Totalnumberofwaystoselect12peoplefrom24=^{27}C_{12}$$=\frac{27!}{12!(15!)}$$=\frac{27\times26\times25\times24\times23\times22\times21\times20\times19\times18\times17\times16\times15!}{12\times11\times10\times9\times8\times7\times6\times5\times4\times3\times2\times1\times15!}$$=3\times13\times23\times3\times20\times19\times17$$=17383860$$NO\text{ of ways to select 12 male=}^{15}x_{12}$$=\frac{15!}{12!(3!)}$$=\frac{15\times14\times13\times12!}{12!3!}$$=5\times7\times13$$=455$

Probability of selecting the 12 males is P(A)

$P(A)=\frac{455}{17383860}$$P(A)=\frac{7}{267444}$