A property has a 10% chance of containing oil, making it worth $1 million, a 30% chance of containing coal, making it worth $500,000, and if no resources are found, it can be sold for $200,000. What is the expected value of this property?

Free worked solution · Quant Blueprint

$370,000, treating oil, coal and neither as mutually exclusive outcomes.

1. Under that interpretation, neither resource occurs with probability 1 − 0.1 − 0.3 = 0.6.
2. Weight each property valuation by its probability: 0.1 × $1,000,000 + 0.3 × $500,000 + 0.6 × $200,000.
3. Add $100,000 + $150,000 + $120,000 = $370,000. These are total property values, not resource bonuses.

Common mistake

If oil and coal can coexist, the given data do not specify the joint probability or combined valuation. State the exclusivity assumption rather than silently treating overlapping events as separate outcomes.

Follow-up

If the property costs c and there are no other costs, the risk-neutral expected profit is $370,000 − c; a positive expectation does not remove risk.

Original educational explanation for this practice question. Reviewed 2026-10-13. Firm-style practice; the label describes the collection’s preparation context.