Analyze decisions and strategies with probability concepts in applied settings.
Find the expected value of a game from its outcomes and probabilities
Problem
First compute the expected gross payout \(5(1/6)+0(5/6)\), then subtract the \(\$1\) cost to obtain expected net value.
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What this problem is really about
Expected net value combines probability-weighted payouts and the certain cost of playing. We’ll multiply each gross payout by its probability, add those contributions, and subtract the entry fee only after finding the expected gross amount. Checking that outcome probabilities sum to one and retaining dollar units verifies the long-run average calculation.
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