Consider that you have two automobiles and the probability of starting each of them is 0.8 on cold mornings. Determine the expected number of days neither car will start during the year if there are...

Consider that you have two automobiles and the probability of starting each of them is 0.8 on cold mornings. Determine the expected number of days neither car will start during the year if there are 100 cold days during the year.

The following appeared as a question to Marilyn Vos Savant in the Parade Magazine (Savant 1991): ‘‘Suppose you’re on a game show, and you’re given a choice of three doors. Behind one is a car; behind the others, goats. You pick a door—say, No. 1—and the host, who knows what’s behind the doors, opens another door—say, No. 3—which has a goat. He then says to you, ‘Do you want to change your selection to door No. 2?’ ’’ Decide whether it is to your advantage to switch your choice.