Alejandro lives in southern California and has a total wealth of $500,000 comprising his home, worth $100,000, and $400,000 in cash. He keeps the cash in a safe deposit box at his local bank, so that it is completely safe. At any given time, there is a 10% chance that his house will be completely destroyed by earthquake and be worth nothing and a 90% chance that nothing will happen to it. Without insurance, the expected value of his end-of-year wealth is:

Question

Quizplus · Accepted Answer

The expected value of Alejandro's end-of-year wealth can be calculated by considering the probabilities of the outcomes for his house. There's a 10% chance his house will be worth $0 and a 90% chance it will retain its $100,000 value. The expected value of the house is thus (0.1 * $0) + (0.9 * $100,000) = $90,000. Adding the $400,000 in cash that is not at risk, the total expected end-of-year wealth is $490,000.

Alejandro Lives in Southern California and Has a Total Wealth