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) ​$80,000B) $87,000C) $97,000D) ​$99,000

Nurul Adiba · Accepted Answer

Final Answer : C, Explanation :  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.

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