A certain club has 10 members including harry one of the 10

A certain club has 10 members, including harry. one of the 10 members is to be chosen at random to be the president, one of the remaining 9 members is to be chosen at random to be the secretary, and one of the remaining 8 members is to be chosen at random to be the treasurer. what is the probability that harry will be either the member chossen to be the secretary or the member chosen to be the treasurer?

Solution

let S be the ssample space associated with chossing a member to be either secretary or treasurer

n(s) = 10C2 = 45

let E1 denotes the event of selecting harry as secretary is 9C1 = 9

let E2 denotes the event of selecting harry as treasure is 8C1 = 8

P(E1) =9/ 45 = 0.2    and P(E2) = 8/ 45 = 0.1778

therefore the probability of selecting harry as either a member to be secretary or as a member to be treasure

P(E1 U   E2) = P(E1) + P(E2)

                     0.2 +0.1778

               = 0.3778