There are 8 job applicants sitting in a waiting room—4 women and 4 men. If 2 of the applicants are selected at random,

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Gmat_mission: Legendary Member; Posts: 1622; Joined: Thu Mar 01, 2018 7:22 amFollowed by: 2 members

by Gmat_mission » Thu Sep 10, 2020 12:14 am

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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. $\dfrac14$

B. $\dfrac37$

C. $\dfrac52$

D. $\dfrac3{14}$

E. $\dfrac1{10}$

Answer: D

Source: Princeton Review

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

Re: There are 8 job applicants sitting in a waiting room—4 women and 4 men. If 2 of the applicants are selected at rando

by Brent@GMATPrepNow » Thu Sep 10, 2020 5:21 am

Gmat_mission wrote: ↑
Thu Sep 10, 2020 12:14 am
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. $\dfrac14$

B. $\dfrac37$

C. $\dfrac52$

D. $\dfrac3{14}$

E. $\dfrac1{10}$

Answer: D

Source: Princeton Review

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

Brent Hanneson - Creator of GMATPrepNow.com

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GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

Re: There are 8 job applicants sitting in a waiting room—4 women and 4 men. If 2 of the applicants are selected at rando

by Brent@GMATPrepNow » Thu Sep 10, 2020 5:22 am

Gmat_mission wrote: ↑
Thu Sep 10, 2020 12:14 am
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. $\dfrac14$

B. $\dfrac37$

C. $\dfrac52$

D. $\dfrac3{14}$

E. $\dfrac1{10}$

Answer: D

Source: Princeton Review

We can also solve this question using counting methods.

P(both selections are women) = (# of outcomes where 2 WOMEN are selected)/(TOTAL # of possible outcomes)

TOTAL # of possible outcomes
Since the order in which we select the two people does not matter, we can use combinations.
We can select 2 people from 8 people in 8C2 ways
8C2 = 28

# of outcomes where 2 WOMEN are selected
Since the order in which we select the two women does not matter, we can use combinations.
We can select 2 women from 4 women in 4C2 ways
4C2 = 6

So, P(both selections are women) = 6/28
= 3/14

Answer: D

Brent Hanneson - Creator of GMATPrepNow.com

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Re: There are 8 job applicants sitting in a waiting room—4 women and 4 men. If 2 of the applicants are selected at rando

by Scott@TargetTestPrep » Mon Sep 14, 2020 4:07 am

Gmat_mission wrote: ↑
Thu Sep 10, 2020 12:14 am
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. $\dfrac14$

B. $\dfrac37$

C. $\dfrac52$

D. $\dfrac3{14}$

E. $\dfrac1{10}$

Answer: D

Solution:

The number of ways to choose 2 applicants from 8 is 8C2 = (8 x 7)/2 = 28.

The number of ways to choose 2 female applicants from 4 is 4C2 = (4 x 3)/2 = 6.

Therefore, the probability that both applicants are women is 6/28 = 3/14.

Alternate Solution:

The probability that the first selection is a woman is 4/8 = 1/2. Assuming a woman is already selected, the probability that the second selection is a woman is 3/7. Thus, the probability that both selections are women is 1/2 * 3/7 = 3/14.

Answer: D

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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