Scatterbrain Samantha often forgets to lock her house.This has caused the probability of a burglary to be 30%.If her house gets broken into,she faces a property loss of $10,000,otherwise she gets to keep her $100,000.What is the minimum price an insurance company could offer (if it had no other costs)?
A)$10,000
B)$3,000
C)$100,000
D)$5,000

Question

​Scatterbrain Samantha often forgets to lock her house.This has caused the probability of a burglary to be 30%.If her house gets broken into,she faces a property loss of $10,000,otherwise she gets to keep her $100,000.What is the minimum price an insurance company could offer (if it had no other costs)?
A)​$10,000
B)$3,000
C)$100,000
D)​$5,000

Quizplus · Accepted Answer

The insurance company can offer the minimum price that will make Samantha indifferent between buying the insurance or not. Suppose the cost of insurance is x. Then the expected value of not buying the insurance is: 
(0.7)*(100000)+(0.3)*(0)= $70,000
The expected value of buying the insurance is: 
(0.7)*(100000-x)+(0.3)*(100000-x-10000)=$73,000-0.3x
Samantha will be indifferent between buying or not if she gets the same expected value with or without insurance:
$70,000=$73,000-0.3x
0.3x=$3,000
x=$10,000/3
Therefore, the insurance company can offer a minimum price of $3,000 to make Samantha indifferent between buying or not buying insurance.

​Scatterbrain Samantha Often Forgets to Lock Her House

Scatterbrain Samantha Often Forgets to Lock Her House