BTGmoderatorLU wrote: ↑

Wed Sep 15, 2021 8:04 am

Source: Princeton Review

There are 8 job applicants sitting in a waiting room, 4 women and 4 men. If 2 of the applicants are selected at random, what is the probability that both will be women?

A. \(\dfrac{1}{4}\)

B. \(\dfrac{3}{7}\)

C. \(\dfrac{5}{2}\)

D. \(\dfrac{3}{14}\)

E. \(\dfrac{1}{10}\)

The OA is D

P(both selected people are women) = P(1st selection is a woman AND 2nd selection is a woman)
= P(1st selection is a woman) x P(2nd selection is a woman)
= 4/8 x 3/7
= 3/14

Answer: D

Aside:
P(1st selection is a woman) = 4/8, since there are 8 people, and 4 of them are women
P(2nd selection is a woman) = 3/7. Once we have selected a woman for the 1st selection, there are 7 people remaining, and 3 of them are women

Cheers,
Brent