Question

In a church wing with 8 men and 10 women members find the probability that a 5 member committee chosen randomly will have.......

Answer 1

Answer:

a) Probability that a 5 member committee will have all men = 0.0065

b) probability that a 5 member committee chosen randomly will have 3 men and 2 women = 0.294

Step-by-step explanation:

Number of men = 8

Number of women = 10

Total number of members = 10 + 8 = 18

Probability = (Number of possible outcomes)/(Total number of outcomes)

Number of ways of selecting a 5 member committee from 18 people = $^{18}C_5 = \frac{18!}{(18-5)!5!} = \frac{18!}{13!5!}$ = 8568 ways

a) Probability that a 5 member committee will have all men

Number of ways of selecting 5 men from 8 men

= $^8C_5 = \frac{8!}{(8-5)!5!} = \frac{8!}{3!5!}$ = 56 ways

Probability that a 5 member committee will have all men = 56/8568

Probability that a 5 member committee will have all men = 0.0065

b)probability that a 5 member committee chosen randomly will have 3men and 2 women​

Number of ways of selecting 3 men from 8 men

=  $^8C_3 = \frac{8!}{(8-3)!3!} = \frac{8!}{5!3!}$ = 56 ways

Number of ways of selecting 2 women from 10 men

=  $^{10}C_2 = \frac{10!}{(10-2)!2!} = \frac{10!}{8!2!}$ = 45 ways

Number of ways of selecting 3 men and 2 women = 56*45

Number of ways of selecting 3 men and 2 women = 2520

Probability of selecting 3 men and 2 women = 2520/8568 = 0.294

probability that a 5 member committee chosen randomly will have 3 men and 2 women = 0.294