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)`
`=(27!)/(12!(15!))`
`=(27*26*25*24*23*22*21*20*19*18*17*16*15!)/(12*11*10*9*8*7*6*5*4*3*2*1*15!)`
`=3*13*23*3*20*19*17`
`=17383860`
`NO\text{ of ways to select 12 male=}^(15)x_(12)`
`=(15!)/(12!(3!))`
`=(15*14*13*12!)/(12!3!)`
`=5*7*13`
`=455`

Probability of selecting the 12 males is P(A)

`P(A)=(455)/(17383860)`
`P(A)=(7)/(267444)`