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What is the probability that a 4-person committee chosen at random fro
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05 Oct 2021, 09:56
05 Oct 2021, 09:56
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What is the probability that a 4-person committee chosen at random from a group consisting of 6 men, 7 women, and 5 children contains at least 1 woman?
A. 11/102
B. 77/204
C. 77/102
D. 91/102
E. 31/34
A. 11/102
B. 77/204
C. 77/102
D. 91/102
E. 31/34
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Re: What is the probability that a 4-person committee chosen at random fro
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05 Oct 2021, 10:08
05 Oct 2021, 10:08
1
Carcass wrote:
What is the probability that a 4-person committee chosen at random from a group consisting of 6 men, 7 women, and 5 children contains at least 1 woman?
A. 11/102
B. 77/204
C. 77/102
D. 91/102
E. 31/34
A. 11/102
B. 77/204
C. 77/102
D. 91/102
E. 31/34
When it comes to probability questions involving "at least," it's best to try using the complement.
That is, P(Event A happening) = 1 - P(Event A not happening)
So, here we get: P(getting at least 1 woman) = 1 - P(not getting at least 1 woman)
What does it mean to not get at least 1 woman? It means getting zero women
So, we can write: P(getting at least 1 woman) = 1 - P(getting zero women)
P(getting zero women) = (number of ways to select 4 people from the 6 men and 5 children)/(total number of ways to select four people from all 18 people)
= (11C4)/(18C4)
= [(11)(10)(9)(8)/(4)(3)(2)(1)]/[(18)(17)(16)(15)/(4)(3)(2)(1)]
= (11)(10)(1)(8)/(2)(17)(16)(15)
= (11)(10)(1)(1)/(2)(17)(2)(15)
= (11)(2)(1)(1)/(2)(17)(2)(3)
= (11)(1)(1)/(17)(2)(3)
= 11/102
So.....
P(getting at least 1 woman) = 1 - 11/102
= 102/102 - 11/102
= 91/102
Answer: D
gmatclubot
Re: What is the probability that a 4-person committee chosen at random fro [#permalink]
05 Oct 2021, 10:08
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