Question

Among the contestants in a competition are 43 women and 21 men. If 3 winners are randomly selected, what Is the probability that they are all men?

Answer 1

Probability that all random selectants are men is (approximately) `3.2%`

Explanation:

If there are `43` women and `21` men then there are `64` people in total.

`P("1st is a man") = 21/64`

`P("2nd is a man"|"1st is a man") = 20/63`

`P("1st and 2nd are men") = 21/64xx20/63`

`P("3rd is a man"|"1st and 2nd are men") =19/62`

`P("all 3 are men") = (21/64xx20/63)xx19/62`

`color(white)("XXXXXXXXXX")~= 0.031922`