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Updated on: 23 Sep 2022, 05:18
Originally posted by Sajjad1994 on 19 Feb 2017, 03:00.
Last edited by Bunuel on 23 Sep 2022, 05:18, edited 2 times in total.
Last edited by Bunuel on 23 Sep 2022, 05:18, edited 2 times in total.
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D
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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. \(\frac{1}{10}\)
19 Feb 2017, 08:58
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SajjadAhmad
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. \(\frac{1}{10}\)
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
19 Feb 2017, 09:05
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SajjadAhmad
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. \(\frac{1}{10}\)
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
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