Question

Eight women and six men apply for a job at Google. Four of the applicants are selected for interviews. Let X denote the number of women in the interview pool. a) Give (explicitly) the probability mass function for X. Also describe a plot of F(x). b) Give (explicitly) the cdf, F(x), for X. Also show a plot of it. c) Determine the probability that more women are interviewed than men.

Answer 1

See below

Explanation:

images attached showing all working

a) The possible values of X are as follows

X = {0,1,2,3,4}

P(x) = P(X=x)

b) The cdf in this case, as in the F(x), comes out to be a step function graph on the basis of values obtained from the probability mass function.

c) To find out the probability when more women are interviewed than me, add together the matrices from when value of X is equal to 2, 3 and 4 (from part a).