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There are 8 job applicants sitting in a waiting room—4 women and 4 men
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06 Oct 2021, 09:16
06 Oct 2021, 09:16
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Question Stats:
82% (00:47) correct
17% (01:39) wrong based on 34 sessions
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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. \(\frac{1}{4}\)
B. \(\frac{3}{7}\)
C. \(\frac{5}{2}\)
D. \(\frac{3}{14}\)
E. \(\frac{1}{10}\)
A. \(\frac{1}{4}\)
B. \(\frac{3}{7}\)
C. \(\frac{5}{2}\)
D. \(\frac{3}{14}\)
E. \(\frac{1}{10}\)
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Re: There are 8 job applicants sitting in a waiting room—4 women and 4 men
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06 Oct 2021, 09:29
06 Oct 2021, 09:29
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Carcass wrote:
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. \(\frac{1}{4}\)
B. \(\frac{3}{7}\)
C. \(\frac{5}{2}\)
D. \(\frac{3}{14}\)
E. \(\frac{1}{10}\)
A. \(\frac{1}{4}\)
B. \(\frac{3}{7}\)
C. \(\frac{5}{2}\)
D. \(\frac{3}{14}\)
E. \(\frac{1}{10}\)
APPROACH #1: 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
APPROACH #2: Probability rules
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
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Re: There are 8 job applicants sitting in a waiting room4 women and 4 men
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23 Mar 2023, 10:55
23 Mar 2023, 10:55
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Expert Reply
Carcass wrote:
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. \(\frac{1}{4}\)
B. \(\frac{3}{7}\)
C. \(\frac{5}{2}\)
D. \(\frac{3}{14}\)
E. \(\frac{1}{10}\)
A. \(\frac{1}{4}\)
B. \(\frac{3}{7}\)
C. \(\frac{5}{2}\)
D. \(\frac{3}{14}\)
E. \(\frac{1}{10}\)
The probability that two women are selected is as follows:
4/8 x 3/7 = 1/2 x 3/7 = 3/14.
Answer: D
