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) $87,000

b) $99,000

c) $97,000

d) $80,000

Answer 1

If she doesn't buy insurance policy ,then

EXPECTED WEALTH= PROB(BURGLARY OCCURS) * WEALTH IF BURGLARY OCCUR + PROB(BURGLARY DOESN'T OCCUR)*WEALTH IF BURGLARY DOESN'T OCCUR

                                   = 0.3 (90000)+0.7(100000)

                                   =27000+70000

                                    =97000

If she buys insurance policy then ,

Her wealth if burglary occurs=100000(initial wealth)-10000(loss due to burglary)-3000(insurance premium payment)+10000(insurance claim) =97000

Her wealth if burglary doesn't occur=100000(initial wealth)-3000(insurance premium payment)=97000

expected wealth = 0.3(97000)+0.7(97000)=97000

So her expected wealth is 97000 irrespective of she buys insurance policy or not.

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