Quandaries and Queries


Problem:  After being rejected for employment, Kim learns that the Bellevue office has hired only two women among the last 20 new employees.  She also learns that the pool of applicants is very large, with an approximately equal number of qualified men and women.  Help her address the charge of gender discrimination by finding he probability of getting two or few women when 20 people are hired, assuming that there is no discrimination based on gender.  Does the resulting probability really support such a charge?



I can show you how to calculate the probability, but you will have to answer the last question on your own.

The assumption is that the pool of qualified applicants is very large with approximately equal numbers of men and women. I am going to select 20 people from the pool at random. The assumption that the pool is large and that the numbers of men and women are approximately equal means that each time I select one of the 20 from the pool, the probability that the persion I select a woman is 1/2 . This is then a binomial experiment with p = 1/2 and n = 20. Let X be the number of women selected, then the probability that two or fewer women are selected is

P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)

Can you use the binomial probability expression to calculate this probability?



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