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Re: Sixty percent of the members of a study group are women, and [#permalink]
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Walkabout wrote:
Sixty percent of the members of a study group are women, and 45 percent of those women are lawyers. If one member of the study group is to be selected at random, what is the probability that the member selected is a woman lawyer?

(A) 0.10
(B) 0.15
(C) 0.27
(D) 0.33
(E) 0.45


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Re: Sixty percent of the members of a study group are women, and [#permalink]
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Video solution from Quant Reasoning:
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Re: Sixty percent of the members of a study group are women, and [#permalink]
To find the probability that a randomly selected member of the study group is a woman lawyer, we need to multiply the probabilities of two independent events: being a woman and being a lawyer.

Given that 60% of the study group are women, the probability of selecting a woman from the group is 0.60 or 60%.

Among the women, 45% are lawyers. Therefore, the probability of selecting a woman lawyer from the group is 0.60 * 0.45 = 0.27 or 27%.

Among the given answer choices, the probability closest to 0.27 is (C) 0.27.
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Re: Sixty percent of the members of a study group are women, and [#permalink]
Why didnt we do 27/60 where 60 is the number of women we have and 27 of them are lawyers?
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Re: Sixty percent of the members of a study group are women, and [#permalink]
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anikpait17 wrote:
Sixty percent of the members of a study group are women, and 45 percent of those women are lawyers. If one member of the study group is to be selected at random, what is the probability that the member selected is a woman lawyer?

(A) 0.10
(B) 0.15
(C) 0.27
(D) 0.33
(E) 0.45

Why didnt we do 27/60 where 60 is the number of women we have and 27 of them are lawyers?


That would give the probability that a member selected from the women is a lawyer. However, the question asks for the probability that a member selected from the entire group is a woman lawyer. Thus, the set you are selecting from is the entire group of 100 members, and the favorable group is the group of women lawyers, which consists of 27 members.

By the way, if you had read the solution above carefully enough, you would catch the mistake you are making.

Hope it's clear.
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Re: Sixty percent of the members of a study group are women, and [#permalink]
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