Question

After being rejected for employment, Kim Kelly learns that the Bellevue Credit Company has hired only two women among the last 17 new employees. She also learns that the pool of applicants is very large, with an approximately equal number of qualified men as qualified women.

Help her address the charge of gender discrimination by finding the probability of getting two or fewer women when 17 people are hired, assuming that there is no discrimination based on gender.
(Report answer accurate to 8 decimal places).
P(at most two) =

Because this is a serious claim, we will use a strict cutoff value for unusual events. We will use 0.5% as the cutoff value (1 in 200 chance of happening by chance). With this in mind, does the resulting probability really support such a charge?

• no, this does not support a charge of gender discrimination
• yes, this supports a charge of gender discrimination

Answer 1

Let X be the number of female employees to be hired in 17 new employees assuming that both male and female are equally eligible to be hired. Then, X ~ Binomial(17, 0.5)

P(at most two) = P(X = 0) + P(X = 1) + P(X = 2)

= ¹⁷C₀ * 0.5⁰ * 0.5¹⁷ + ¹⁷C₁ * 0.5¹ * 0.5¹⁶ + ¹⁷C₂ * 0.5² * 0.5¹⁵

= 0.00000763 + 0.00012970 + 0.00103760

= 0.00117493

Since the resulting probability (0.00117493) is less than 0.005 (0.5%), we can conclude that the serious claim of gender discrimination is valid. So,

yes, this supports a charge of gender discrimination