Compare Strategies Using Expected Value Practice Test

A gamer chooses between two loot boxes to open repeatedly. Net payoff is the value of the item received minus the purchase price.

Strategy A: Costs $4. Outcomes: with probability $0.70$ you get an item worth $5 (net $1); with probability $0.30$ you get an item worth $0 (net $-4).

Strategy B: Costs $4. Outcomes: with probability $0.10$ you get an item worth $30 (net $26); with probability $0.90$ you get an item worth $0 (net $-4).

Which strategy would result in a higher average net payoff over many repetitions?

A company is choosing between two quality-control tests to run on many batches. Payoffs are net dollars to the company per batch.

Strategy A: Test costs $3,000. Outcomes: with probability 0.95 the batch passes and there is no further cost (net payoff $-3,000); with probability 0.05 the test catches a defect and prevents a $100,000 recall (net payoff $100,000-3,000=\$97,000).

Strategy B: Test costs $6,000. Outcomes: with probability 0.98 the batch passes (net payoff $-6,000); with probability 0.02 the test catches a defect and prevents the $100,000 recall (net payoff $94,000).

Which strategy would result in a higher average net payoff over many repetitions?