2. At the Antonio Car dealership, the probability that during a month at least one consumer returns a car for warranty work is 0.45. Suppose that the numbers of cars returned for warranty work in different months are independent. Consider the period until the fifth month in which at least one car was returned for warranty work. What is the probability that, during that period, there were exactly three months with no car returned for warranty work?

Hint: Call a month “success” if, in that month, at least one car is returned for warranty work.