Suppose that the number of years that a used car will run before a major breakdown is exponentially distributed with an average of 0.25 major breakdowns per year. (a) If you buy a used car today, what...

1. Suppose that the number of years that a used car will run before a major breakdown is exponentially distributed with an average of 0.25 major breakdowns per year.

(a) If you buy a used car today, what is the probability that it will not have experienced a major breakdown after 4 years?

(b) How long must a used car run before a major breakdown if it is in the top 25% of used cars with respect to breakdown time?