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

Hence, we want the probability of choosing 2 women.

Let a success be getting a woman.

Note that the probability of x successes out of n trials is          
          
P(x) = C(N-K, n-x) C(K, x) / C(N, n)          
          
where          
N = population size =    5      
K = number of successes in the population =    2      
n = sample size =    3      
x = number of successes in the sample =    2      
          
Thus,          
          
P(   2   ) =    0.3 [ANSWER]

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