2. You purchase an insurance policy that covers a gas furnace for one year. During thatyear, at most one of the three problems can occur:

The igniter switch may need to be replaced at a cost of$60.

There is a 0.10probability of this.

The pilot light may need to be replaced at a cost of$200. There is a 0.05 proba-bility of this.

The furnace may need to be replaced at a cost of$3000. There is a 0.01 probabilityof this.

(a) What is the probability that you will not have to make a claim for the duration ofyour policy?

(b) What is the expected amount of money that you will claim from the insurancecompany?

(c) (Bonus) The insurance company charges you$30 for this policy. Do you think it'sworth it?