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.If Samantha is offered an insurance policy for her house to protect her from loss at $3,000,what is her expected wealth?
A)$80,000
B)$87,000
C)$97,000
D)$99,000

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.If Samantha is offered an insurance policy for her house to protect her from loss at $3,000,what is her expected wealth?
A)​$80,000
B)$87,000
C)$97,000
D)​$99,000

Quizplus · Accepted Answer

Samantha's expected wealth without insurance is calculated as follows: 70% chance of no burglary (0.7 * $100,000) + 30% chance of burglary (0.7 * $100,000 - 0.3 * $10,000) = $97,000. With the insurance costing $3,000, her expected wealth remains $97,000 because the insurance offsets the potential loss from burglary.

​Scatterbrain Samantha Often Forgets to Lock Her House

Scatterbrain Samantha Often Forgets to Lock Her House