Andres, Beth and Charlie do cold call sales for their investment firm. Today they’ve made a little bet. The first one to talk to a “live” person when they make a call wins. They will call sequentially, with Andres going first, Beth going second, and Charlie going third, and will continue calling in this order until one of them gets a “live” person on the line. Based on past experience, the three agree that the likelihood of a call being answered by a “live” person is about 20%.
a) What are the respective chances of winning for the three sales people?
b) How likely is it that Beth will win on her third call?
c) Show the probability distribution for the random variable “number of calls made to determine a winner.”
d) What is the expected number of calls that will have to be made to declare a winner?