Answer:
0.18% probability that they are all women
Step-by-step 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:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
Desired outcomes:
3 women, from a set of 13. So
[tex]D = C_{13,3} = \frac{13!}{3!(13 - 3)!} = 286[/tex]
Total outcomes:
3 senators, from a set of 100. So
[tex]T = C_{100,3} = \frac{100!}{3!(100 - 3)!} = 161700[/tex]
Probability;
[tex]p = \frac{D}{T} = \frac{286}{161700} = 0.0018[/tex]
0.18% probability that they are all women
