sandy wrote:

Of the 700 members of a certain organization, 120 are lawyers. Two members of the organization will be selected at random. Which of the following is closest to the probability that neither of the members selected will be a lawyer?

A. 0.5

B. 0.6

C. 0.7

D. 0.8

E. 0.9

A student asked me to solve this question (and answer a few other questions). So, here it goes...

SOLUTION #1: Probability rulesQuestion: Are we selecting people with replacement or without replacement?We're told that

two members are selected, so we can assume that the two members are

different.

In other words, we're selecting people without replacement.

ASIDE: If this were my question, I would have written "two DIFFERENT members will be selected..." to be free from ambiguity. That said, this is an official question, so this is what we have to go with.Of the 700 members of a certain organization, 120 are lawyers. So we have 120 lawyers

And we have 580 non-lawyers

Two members of the organization will be selected at random. Which of the following is closest to the probability that neither of the members selected will be a lawyer?P(neither selection is a lawyer) = P(1st selection is non-lawyer

AND 2nd selection is non-lawyer)

= P(1st selection is non-lawyer)

x P(2nd selection is non-lawyer)

= 580/700

x 579/699

≈ 0.69

Answer: C

ASIDE: I should also mention that, if we were to treat this question as a replacement question, we'd still get the same answer, since the value of 579/699 is very close to the value of 580/700Cheers,

Brent

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Brent Hanneson – Creator of greenlighttestprep.com

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