A division of a company consists of seven men and five women

Question

A division of a company consists of seven men and five women. If two of these twelve employees are randomly selected as representatives of the division, what is the probability that both representatives will be female?
(A) 1/6
(B) 2/5
(C) 2/9
(D) 5/12
(E) 5/33

For a full discussion of probability questions that involve counting techniques, and for a full solution to this particular question, see this post:
https://magoosh.com/gmat/2013/gmat-proba ... echniques/
For some shortcuts for doing these calculations without a calculator, see this post:
https://magoosh.com/gmat/2012/gmat-math- ... binations/

Show Answer

Official Answer

E

sambam · Accepted Answer

Total number of ways to select 2 members from 12 members = 12C2 - denominator
Total number of ways to select 2 females from 5 total females = 5C2 - numerator

Therefore probability of having 2 females reps is 5C2 / 12C2 = 5/33 (E)

holidayhero · Answer

A different way.

There are a total of 12 employees (7 men and 5 women)

Probability of 1st person selected being a woman is 5/12
Probability of the 2nd person selected being a woman is 4/11 (4 women left in the 11 remaining employees)

Probability of 1st and 2nd selected both being women 
=5/12 X 4/11
= 20/132
which reduces to 
= 5/33

Answer E

usre123 · Answer

Hello, why don't we multiply the final answer with 2? Because there are two ways in which we can accomplish this.

LighthousePrep · Answer

usre123 ,

The reason we don't have to multiply by two in the solution is because we are drawing from the same pool. In the example you are thinking ( https://gmatclub.com/forum/john-has-on-his-shelf-four-books-of-poetry-145499.html ), there are two different pools to choose from, novels and reference. In this case, the only pool we're picking from is the pool of women. Of the two picks, we want the first to be a woman, and the second to be a woman. There is no way to "flip" this selection, as the "flip" is the same as our original scenario. In the other problem, the reason we have to multiply by two is because we have two outcomes, the first selection is a novel and the second is a reference, or the first is a reference and the second is a novel.

Hope this makes sense!

usre123 · Answer

awesome, thanks! Now it's perfectly clear

BrainLab · Answer

Hi everyone, here's my solution for Example 2:
We have 7 males + 5 females = 12

The probability that the first choice will be a woman is 5/12 (females/all)
The probability that the second choice will be a woman is 4/11 (for the second run we have 4 women and 11 Persons left)

5/12*4/11 = 5/33

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A division of a company consists of seven men and five women

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A division of a company consists of seven men and five women

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