Expected Value — Which Choice Is Fairer? (Grades 7–8)
Expected value tells you the average payoff of a choice over the long run: multiply each prize by its probability. For a single prize, expected value = probability × prize. Comparing two offers, the one with the higher expected value is the better bet. Offer A: 3/5 chance at 100 → EV = 60. Offer B: 3/10 chance at 250 → EV = 75. B is better.
Understanding expected value
Expected value tells you the average payoff of a choice over the long run: multiply each prize by its probability. For a single prize, expected value = probability × prize. Comparing two offers, the one with the higher expected value is the better bet. Offer A: 3/5 chance at 100 → EV = 60. Offer B: 3/10 chance at 250 → EV = 75. B is better.
Key Idea
Expected value tells you the average payoff of a choice over the long run: multiply each prize by its probability. For a single prize, expected value = probability × prize. Comparing two offers, the one with the higher expected value is the better bet. Offer A: 3/5 chance at 100 → EV = 60. Offer B: 3/10 chance at 250 → EV = 75. B is better.
Seeing it in action
Worked example
A game: 3/5 chance to win 100 points. Expected value?
EV = 3/5 × 100 = 60 points.
Expected value = probability × payoff.
Try a few
1/4 chance at 80 — EV?
1/2 chance at 50 — EV?
Which is better: 1/3 of 90, or 1/2 of 50?
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