Statistics

An automobile insurance company estimates the following damage probabilities for the next year on a $25,000 automobile

Total loss = 0.001
50% loss = 0.01
25% loss = 0.05
10 % loss = 0.10

Assuming the company will sell only a $500 deductible policy for this model (i.e. the owner covers the first $500 in damages), how much annual premium should the company charge in order to average $480 profit per policy sold?

Sorry, I missed this one. I hate to miss ones like this.

First, let's add things up.

0.001 + 0.01 + 0.05 + 0.10 = 0.161

This appears to leave P(no loss) = 1 - 0.161 = 0.839

Then the whole universe

P(0.00 loss * 25000) = 0.839 = P($0 loss) <== Company pays $0
P(0.10 loss * 25000) = 0.100 = P($2500 loss) <== Company pays $2000
P(0.25 loss * 25000) = 0.050 = P($6250 loss) <== Company pays $5750
P(0.50 loss * 25000) = 0.010 = P($12500 loss) <== Company pays $12000
P(1.00 loss * 25000) = 0.001 = P($25000 loss) <== Company pays $24500

Total Expectation: ($0 * 0.839) + ($2000 * 0.100) + ($5750 * 0.050) + ($12000 * 0.010) + ($24500 * 0.001) = $632.00 = Expected Break Even Premium

Now, what do you suppose would be the make Premium expected to produce $480 in profit?