Given: Song owns a $300K house and has a 10% 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.

Problem:

Trevone, who owns the same type of house and faces the same probability distribution of losses as Song, also purchases full insurance for an actuarially fair premium from Lemonade Insurance Company. We assume that the two houses are independent of each other. In other words, if one house has a fire, this has no impact on the probability of the other house having a fire.

What is the probability distribution of total losses for Lemonade Insurance Company if they sell contracts to both Song and Trevone? 

What is the expected loss or expected payout for Lemonade Insurance Company if they sell contracts to both Song and Trevone? 

What is the amount of risk Lemonade Insurance Company faces if they sell contracts to both Song and Trevone? 

Briefly explain the benefit(s) to Lemonade Insurance Company as the number of insurance contracts sold increases?