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
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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P(both selected people are women) = P(1st selection is a woman AND 2nd selection is a woman)Gmat_mission wrote: ↑Thu Sep 10, 2020 12:14 amThere 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(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
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We can also solve this question using counting methods.Gmat_mission wrote: ↑Thu Sep 10, 2020 12:14 amThere 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 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
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Solution:Gmat_mission wrote: ↑Thu Sep 10, 2020 12:14 amThere 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
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
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