A local company has been in trouble recently over hiring male applicants rather

Question

A local company has been in trouble recently over hiring male applicants rather than female applicants. The problem became apparent when three employees hired were all male, even though the six applicants for the three positions included three females. That probability is 0.05. The company claims to have cleaned up their act, showing the even more recent hiring round to have included two women and one man in a pool of 5 applicants consisting of 2 women and 3 men. What is the probability of such a choice pattern?

Explanation / Answer

there are all total 5 applicants out of which 2 are women and 3 are men.

2 women and 1 man have been selected.

so out of 5 people 3 are selected in 5C3 ways with 2 women are selected from 2 women in 2C2 ways and 1 man is selected from 3 men in 3C1 ways.

hence the probability of such a choice pattern is= total number of ways in which 2 women and 1 men can be selected out of 2 women and 3 men/total number of ways of selecting 3 persons from 5 persons

=2C2*3C1/5C3=0.3 [answer]

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