Question

A jury pool consists of 12 angry people and 8 chill people. How many 12 member juries:Can be made?Consist of 7 chill and 5 angry people?Consist of at least 10 angry people?

Answer 1

Given that the number of angry people=12 and the number of chill peoples=8.

The total number of peoples=The number of angry people + the number of chill people.

The total number of people in juries=12+8=20

Let A be an event that made 12 members of juries consists of 7 chill and 5 angry people.

The probability of A =P(A)

`P(A)=(8C_7+12C_5)/(20C_(12))`

`=((8!)/(7!(8-7)!)+(12!)/(5!(12-5)!))/(20!)/(12!(20-12)!)`

`=((8*7!)/(7!)+(12*11*10*9*8*7!)/(5*4*3*2*(7)!))/(20*19*18*17*16*15*13*12!)/(12!*8*7*6*5*4*3*2)`

`=800/8997.857=0.0889`
`P(A)=0.09`

Hence only one 12 member jury pool can be made that consist of 7 chill and 5 angry people.

Hence the answer is 1.