Exercises: Evaluate and Compare Strategies Using Expected Values

You are comparing two strategies by their expected annual cost (in dollars). Strategy X has an expected cost of $\text{\char"0024}950$ and Strategy Y has an expected cost of $\text{\char"0024}1{,}237.50$. Which strategy should you recommend, and why?

A prize wheel costs $\text{\char"0024}5$ to spin. It pays $\text{\char"0024}20$ with probability $0.3$ and $\text{\char"0024}0$ with probability $0.7$. Model this as a NET payoff (winnings minus the $\text{\char"0024}5$ cost). What is the expected net payoff, in dollars? Enter a number (use a negative sign if it is a loss).

To compare two competing strategies, you model each one as its own   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   distribution, compute each strategy's   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲     ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   , and then compare those values. (First blank: "payoff or cost". Second and third blanks: the two-word name of the average you compute.)

An auto policy has a $\text{\char"0024}1{,}200$ annual premium and a $\text{\char"0024}250$ deductible paid per accident. For this driver the chance of having at least one accident (which triggers the full deductible) is $0.15$. The expected annual cost is the premium plus the expected out-of-pocket payment. Compute the expected annual cost, in dollars.

Two prize wheels each cost the same to play. Wheel P has an expected PAYOFF of $\text{\char"0024}8$. Wheel Q has an expected PAYOFF of $\text{\char"0024}11$. Which wheel should you choose to maximize winnings, and why?

Policy B has an $\text{\char"0024}800$ annual premium and a $\text{\char"0024}1{,}000$ deductible paid per accident. For a driver whose chance of an accident is $0.15$, compute the expected annual cost, in dollars.

For a given driver, Policy A has an expected annual cost of $\text{\char"0024}1{,}237.50$ and Policy B has an expected annual cost of $\text{\char"0024}950$. Which policy do you recommend?