Brittany owns a $400,000 house, which has a 1% chance of experiencing a fire in any given year. Assume that if a fire occurs, the house is completely destroyed.

For the peril of Brittanys house burning down the Expected Loss (P*) = $4,000

The amount of risk that Brittany faces (for the peril of her house burning down), as measured by the Measures of Dispersion that we learned about back in Topic #4, is as follows:

• Standard Deviation = $39,799.50
• Coefficient of Variation = 9.95 or 995%

Brittany purchases full insurance from Schwartz Insurance Company to insure her home against the peril of fire. Assume that the premium charged by Schwartz Insurance Company is equal to the actuarially fair premium (AFP)

• Meaning, the quote from Schwartz Insurance Company = Brittanys Expected Loss (P*)
• Meaning, the quote from Schwartz Insurance Company = $4,000

Question #1:

Assume Brittanys twin sister Brooke owns the same exact type of house (worth $400,000) and faces the same exact probability of her house burning down to the ground (1%). 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.

Like Brittany, Brooke also purchases full insurance from Schwartz Insurance Company.

Schwartz Insurance Company determines the possible outcomes and corresponding probabilities that could occur if it sells full insurance contracts to BOTH Brittany AND Brooke:

Outcome	Loss $ Amount	Probability
Both houses do NOT burn down	$0	0.99 * 0.99 = 0.9801
Brittanys house burns down; AND Brookes house does not burn down	$400,000	0.01 * 0.99 = 0.0099
Brookes house burns down; AND Brittanys house does not burn down	$400,000	0.01 * 0.99 = 0.0099
Both houses burn down	$800,000	0.01 * 0.01 = 0.0001
		1.00

P* calculation

(0*0.9801) +(400000*0.0099) +(400000*0.0099) +(800000*0.0001) = 8,000

Schwartz Insurance Company calculates that the Expected Loss for the entire risk pool (containing both Brittany and Brooke) = $8,000. Schwartz Insurance Company are professionals, so you can rest assured that the calculated Expected Loss is 100% accurate (meaning you do NOT need to calculate it!)

1. Schwartz Insurance Company calculates that the risk pool containing BOTH Brittany and Brooke have a standard deviation = $56,285. Again, Schwartz Insurance Company are professionals, so you can rest assured that the calculated standard deviation is 100% accurate (meaning you do NOT need to calculate this either!)

2. What is the amount of risk Schwartz Insurance Company faces if it sells full insurance contracts to BOTH Brittany AND Brooke? [2 points]