# What is the probability that the minority applicant is chosen for the positions in the following case.Four equally qualified people apply for two identical positions in a company.One and only one...

What is the probability that the minority applicant is chosen for the positions in the following case.

Four equally qualified people apply for two identical positions in a company.One and only one applicant is a member of a minority group.The positions are filled by choosing two of the applicants at random.

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### 1 Answer

There are four equally qualified applicants of which only one is from a minority group. There are two positions to be filled and the applicants are chosen at random.

Two cases are possible here, the minority applicant is chosen for the first position or the minority applicant can be chosen for the second position.

To fill the first position, there is one minority applicant and 3 others. the probability that the minority applicant is chosen is 1/4.

In case the minority applicant is not chosen for the first post, there are 2 applicants left who do not belong to the minority and one minority applicant. The probability that the minority applicant is chosen here is 1/3.

Considering both positions the probability that the minority applicant is chosen are (1/4) + (1/3) = 7/12

**The required probability that the minority applicant is chosen are 7/12.**