Question

A jury pool consists of 31 people, 13 men and 18 women. Compute the probability that a randomly selected jury of 12 people is all male.

Answer 1

The first person you select has a probability of

`(13)/(31)`

of being a male. The second time, there is a probability of:

`(12)/(30)\text{.}`

Following the same reasoning, the probability of selecting 12 males is:

`(13)/(31)\cdot(12)/(30)\cdot(11)/(29)\cdot(10)/(28)\cdot(9)/(27)\cdot(8)/(26)\cdot(7)/(25)\cdot(6)/(24)\cdot(5)/(23)\cdot(4)/(22)\cdot(3)/(21)\cdot(2)/(20)\text{.}`

Simplifying the above multiplication, we get:

`(13!)/(31\cdot30\cdot29\cdot28\cdot27\cdot26\cdot25\cdot24\cdot23\cdot22\cdot21\cdot20)\approx9.2*10^(-8)\text{.}`

Answer:

`9.2*10^(-8)=0.000000092.`