Question

. In the 107th Congress, the Senate consists of 13 women and 87 men. If a lobbyist for the tobacco industry randomly selects three different senators, what is the probability that they are all women

Answer 1

0.18% probability that they are all women

Explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

The order in which the senators are chosen is not important, so the combinations formula is used to solve this question.

Combinations formula:

`C_(n,x)` is the number of different combinations of x objects from a set of n elements, given by the following formula.

`C_(n,x) = (n!)/(x!(n-x)!)`

Desired outcomes:

3 women, from a set of 13. So

`D = C_(13,3) = (13!)/(3!(13 - 3)!) = 286`

Total outcomes:

3 senators, from a set of 100. So

`T = C_(100,3) = (100!)/(3!(100 - 3)!) = 161700`

Probability;

`p = (D)/(T) = (286)/(161700) = 0.0018`

0.18% probability that they are all women