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 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.What is her expected wealth?
A)​80,000
B)$87,000
C)$97,000
D)​$99,000

Quizplus · Accepted Answer

The expected wealth can be calculated by taking the weighted average of the outcomes based on their probabilities. If her house is burglarized (30% chance), she loses $10,000, leaving her with $90,000. If it's not burglarized (70% chance), she keeps her $100,000. Thus, the expected wealth is (0.3 * $90,000) + (0.7 * $100,000) = $27,000 + $70,000 = $97,000.

​Scatterbrain Samantha Often Forgets to Lock Her House

Scatterbrain Samantha Often Forgets to Lock Her House