Back to Find the expected payoff for a game of chance — Problem 5 · Task Set 31

Exercises: Find the Expected Payoff for a Game of Chance

Work through each section in order. The payoff of an outcome is its NET value: the prize received minus the cost to play. The cost to play is subtracted from EVERY outcome, win or lose. The expected payoff is the sum of each net payoff times its probability. Its sign classifies the game: favorable to the player if positive, fair if zero, unfavorable if negative. Always include the "win nothing" outcome and make the probabilities sum to 1.

Grade 11·20 problems·~35 min·Common Core Math - HS Statistics and Probability·standard·hss-md-b-5a

Work through problems with immediate feedback

Fluency Practice

Build the signed net-payoff table when asked, then compute and classify the expected payoff.

A game has expected payoff $E = -\text{\char"0024}0.40$ per play to the player. How should the game be classified, and what does the number mean?

Unfavorable to the player; on average the player loses about $0.40 per play.

Favorable to the player; on average the player gains $0.40 per play.

Fair; the expected payoff is small enough to count as zero.

Unfavorable; the player loses exactly $0.40 on every single play.