58 Six men and five women apply for a job at Alpha Inc Three

5.8 Six men and five women apply for a job at Alpha, Inc. Three of the applicants are selected for interviews. Let X denote the number of women in the interview pool. a) What are the possible values of the random variable X? b) Obtain the number of interview pools corresponding to each possible value of X; that is, corresponding to each possible value of X; th for each possible value x of X, find the number of ways that event (X can occur. c) Describe the event (X 1) in words and find the number of ways in which it can occur.

Solution

possible values X are (0,1,2,3)

number of interview pools

Pool 0: 0 women and 3 men

Pool1: 1 women and 2men

Pool 2: 2 women and 1 men

Pool 3: 3 women 0 men

X<1 corresponds to Pool 0 and 1