Question: A furnace company provides a guarantee to its customers: if their newly purchased furnace fails within one year, the company will return 100% of the initial cost to the customer; if the furnace fails between 1 and 5 years of ownership, the company will return 40% of the initial cost to the customer; and if the furnace fails between 5 and 10 years of ownership, the company will return 10% of the initial cost to the customer. The probability of a furnace failing in the first year is 0.05; the probability of a furnace failing between 1 and 5 years is 0.20; and the probability of of a furnace failing between 5 years and 10 years after purchase is 0.35.

a) If a person purchases a new furnace, what is the probability that it will survive beyond 10 years?

b) If the company sells 100 furnaces tomorrow for $500 each, what percentage of their earnings should they expect to return to these 100 customers within 10 years?

c) After 10 years, you randomly call up 3 of the 100 customers you sold furnaces to in part b). What is the probability that all 3 of the customers you call report that their furnaces are still operating?