1. Rhoda Ruyner owns a $200,000 home and has a 2% chance of experiencing a loss that destroys her home in any given year. Assume that only one loss per year can occur and that if a loss occurs, her home is totally destroyed. Suppose that Rhoda purchases a full insurance contract from Acme Insurance for an actuarially fair premium. This contract would pay losses due to the total destruction of Rhodas home. Assume that Rhodas contract is the only insurance contract that Acme Insurance sold. What is the actuarially fair premium that Acme Insurance will charge Rhoda in the coming year? Show all calculations.

2. Wile E., who owns the same type of house and faces the same loss distribution as Rhoda in the question above, also purchases full insurance for an actuarially fair premium from Acme Insurance. We assume that the two houses are independent of one another. Show all calculations.
   1. Create a probability distribution table of possible outcomes for Acme Insurance if Acme sells insurance to both Rhoda and Wile E.

2. What is the expected loss for Acme Insurance if Acme sells insurance to both Rhoda and Wile E.?

3. Now suppose Wile E. has a 4% chance of experiencing a total loss in any given year. Suppose Acme Insurance still offers Wile E. and Rhoda the same insurance contract and charges them the same premium; in other words, Acme Insurance put Rhoda and Wile E. into the same risk pool. Show all calculations.
   1. Create a probability distribution table of possible outcomes for Acme Insurance if Acme sells insurance to both Rhoda and Wile E.

2. What premium amount must Wile E. and Rhoda each individually pay if Acme Insurance wants to break-even?

3. Will Wile E. purchase this contract if he is charged the break-even premium? Will Rhoda purchase this contract if she is charged the break-even premium? Briefly explain your reason.