On this problem, it is possible that hiring all males would be gender bias, but hiring all females is not gender bias. The reason for this is that we have many more females that applied for the jobs (19 females  and 8 males). Therefore, the probability of at least one female hired would be higher than the probability of at least one male hired. 5. What is the probability that at least one male is hired?    6. What is the probability that at least one female is hired?    7. What is the probability that two are female?

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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On this problem, it is possible that hiring all males would be gender bias, but hiring all females is not gender bias. The reason for this is that we have many more females that applied for the jobs (19 females  and 8 males). Therefore, the probability of at least one female hired would be higher than the probability of at least one male hired.

5. What is the probability that at least one male is hired?   

6. What is the probability that at least one female is hired?   

7. What is the probability that two are female?   

Expert Solution
Step 1

It is given that in the hiring process, there are 19 females and 8 males.

Consider that p1 and p2 are defined as the probabilities of females and males are hired, respectively.

Thus,

Probability homework question answer, step 1, image 1

Step 2

Consider that X is a random variable, defined as the number of individuals get a job, and follows a binomial distribution with p success rate and n number of people.

Probability homework question answer, step 2, image 1

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