Calculating Expected Winnings

Pre-Algebra · Axiom Academy

EXAMPLE Calculating Expected Winnings Work out the expected value of a paid game and decide whether it's worth playing. A carnival game costs 2 to play. You draw once and win one of the prizes below. What is the expected value of one play — on average, do you come out ahead, behind, or even? Nice work! You computed an expected value from scratch and used it to judge a game. Here's what to carry forward: Expected value: multiply each prize by its probability, then add the results together. Include every outcome: even "win nothing" belongs in the sum — its term is 0 × 0.7 = 0 , but you still account for it. Subtract the cost: the net expected value is expected winnings minus what you pay to play. Read the sign: here expected winnings ( 2 ) equal the cost ( 2 ), so the net is 0 — a fair game. A positive net favors you, a negative net favors the house, and a net of 0 (like this game) is mathematically fair. The same calculation evaluates lottery tickets, insurance, and everyday bets.

This is the written version of the interactive lesson above. See the full Pre-Algebra course.