1) An electric car contains 2,500 components, each component fails independently from the others and the yearly failure probability per component is 0.002. (a) What is the probability that all components are working at the end of one year? (b) What is the probability that three or more components fail before the end of the year?

2) Assume that the life-span of a heating/cooling system has an exponential distribution and

its mean is 11 years,

(a) What is the probability that the system will last more than 11 years?

(b) If a manufacture offers a 2-year guarantee replacement warranty, what is the probability

that a replacement will be made?