A team of 5 analysts is about to examine the earnings prospe

A team of 5 analysts is about to examine the earnings prospects of 20 corporations. Each of the 5 analysts will study 4 of the corporations. These analysts are not equally competent. In fact, one of them is a star, having an excellent record of anticipating changing trends. Ideally, management would like to allocate the 4 corporations whose earnings will deviate most from past trends to this analyst. However, lacking this information, management allocates corporations to analysts randomly. What is the probability that at least 2 of the 4 corporations whose earnings will deviate most from past trends are allocated to the star analyst?

Solution

Let X be the number of the four corporations whose earnings will deviate most from past trendsare allocated to the star analyst. Then X has a hypergeometric distribution: n=5 (number of trials), N=20 (population size) and s=4 (number of possible occurences). Need to find P(X2) = 1- P(0)- P(1) = 1 – 0.37564 – 0.46233 = 0.16202