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In a certain corporation, there are 300 male employees and 100 female employees. It is known that 20% of the male employees have advanced degrees and 40% of the females have advanced degrees. If one of the 400 employees is chosen at random, what is the probability this employee has an advanced degree or is female?

Re: In a certain corporation, there are 300 male employees and 100 female [#permalink]

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04 Mar 2015, 10:37

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Yup, the answer is 2/5. D.

The explanation was provided as below.

Bunuel wrote:

In a certain corporation, there are 300 male employees and 100 female employees. It is known that 20% of the male employees have advanced degrees and 40% of the females have advanced degrees. If one of the 400 employees is chosen at random, what is the probability this employee has an advanced degree or is female?

Re: In a certain corporation, there are 300 male employees and 100 female [#permalink]

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04 Mar 2015, 13:18

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Answer is D.....

we are told that 20% of male have advanced degree and also 40% of women....

so, 20% * 300 + 40% * 100 = 60 + 40= 100 total number of advanced degree holders,

Here is TWO approaches : First , The problem wants the probability of selecting ONE employee OUT of 400 employees who has advanced degree OR female

so we have counted the total number of degree holders ( 100 ) and we should add this number with the remaining number of females ( 100 -40 =60 )

So we have 100 + 60 =160 total our favorite outcomes so , probability is = Total favorite out comes / total out comes = 160/ 400 = 16/ 40 = 2/5 answer D

Second approaches : a little bit difference : 100/400 ( total advanced holders to total people ) + 60 / 400 ( the remaining females who don't have degree but are female) = 100/400 + 60/400 = 1/4 + 6/40 = 2/5

Important point: THE problem says that total number of degree holders OR female , here OR is so important it means we must add two fractions toghether , if the problem said AND we must multiple two fraction .... so answer D....

There is a minor issue with the "intent" of this question. I'm going to assume that the author is asking for the probability of selecting an employee who has an advanced degree or who is female OR BOTH.

In this scenario, there's actually some math that can be avoided. There are 100 females; some have advanced degrees and some don't, but performing THAT calculation is irrelevant because there will be 100 females regardless. We also have to factor in the number of men with advanced degrees, which is (.2)(300) = 60.

In a certain corporation, there are 300 male employees and 100 female employees. It is known that 20% of the male employees have advanced degrees and 40% of the females have advanced degrees. If one of the 400 employees is chosen at random, what is the probability this employee has an advanced degree or is female?

In this corporation, there are 400 total employees. There are 100 women. Of the 300 men, 20% have advanced degrees —-10% of 300 must be 30, so 20% of 300 must be 60. Add the women and the men with advanced degrees: 100 + 60 = 160. This is the OR region, full set of individuals that satisfy the condition “has an advanced degree or is female.” Of the 400 employees, what’s the probability of picking one of the 160 in this particular group? P = 160/400 = 16/40 = 4/10 = 2/5.

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In a certain corporation, there are 300 male employees and 100 female employees. It is known that 20% of the male employees have advanced degrees and 40% of the females have advanced degrees. If one of the 400 employees is chosen at random, what is the probability this employee has an advanced degree or is female?

A. 1/20 B. 1/10 C. 1/5 D. 2/5 E. 3/4

Kudos for a correct solution.

Since 20% of the male employees have advanced degrees, 0.2 x 300 = 60 male employees have advanced degrees and 300 - 60 = 240 male employees do not have advanced degrees.

Since 40% of the female employees have advanced degrees, 0.4 x 100 = 40 female employees have advanced degrees and 100 - 40 = 60 female employees do not have advanced degrees.

So, 60 + 40 = 100 employees have an advanced degree.

Thus, the probability of selecting an employee who is female or has an advanced degree is:

P(women) + P(advanced) - P(both)

100/400 + 100/400 - 40/400

160/400 = 16/40 = 2/5

Answer: D
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