Question

The annual premium for a $5000 insurance policy against the theft of a painting is $150. If the (empirical) probability that the painting will be stolen during the year is .01, what is your expected return from the insurance company if you take out this insurance and repeat problem from the point of view of the insurance company.

Answer 1

let X be the net return to you

P(X=5000-150=4850) =P(stolen )=0.01

P(X=-150) =P(not stolen )=1-0.01 =0.99

expected return from the view of you E(x)=xP(x)

=4850*0.01-150*0.99 =$ -100

for Insurance company:

let X be the net return to insurance company:

P(X=150) =P(not stolen )=1-0.01 =0.99

P(X=150-5000=-4850) =P(stolen )=0.01

expected return from the view of insurance company E(x)=xP(x)

=150*0.99-4850*0.01 =$100