Song owns a $250,000 house and has a 2% chance of experiencing a fire in any given year. Assume that only one fire per year can occur and that if a fire occurs, the house is completely destroyed. Suppose that Song purchases a full insurance contract from Lemonade Insurance Company for an actuarially fair premium. This contract would pay all losses due to the fire. Assume that Song's contract is the only insurance contract Lemonade Insurance Company sold.

Now suppose Tyler owns a $550,000 house and has a 2% chance of experiencing a fire in any given year. Assume as before that the fire will result in a total loss. Suppose the Lemonade Insurance Company offers Song and Tyler the same insurance contract and charges them the same premium. In other words, they put Song and Tyler into the same risk pool.

a. What is the probability distribution of total losses for Lemonade Insurance Company if they sell contracts to Song and Tyler? (2 points)

b. What premium must Lemonade Insurance Company charge each of Song and Tyler if they want to 'break even'? (2 points)

c. Will Song purchase this contract if he is charged the 'break-even' premium? Will Tyler purchase this contact if he is charged the 'break-even' premium? Briefly explain your reason. (2 points)

d. What is the amount of risk Lemonade Insurance Company faces if they sell contracts to both Song and Tyler? (2 points)