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There are two different raffles you can enter. In raffle A, one ticket out of 100100 will win a $370\$370 prize. The other tickets will win nothing. Each ticket costs $15\$15. Raffle B, which is for a fundraiser, has 200200 tickets. Each ticket costs $16\$16. One ticket will win a $680\$680 prize, and the remaining tickets will win nothing. Which raffle is a better deal?\newline(A)Raffle A\newline(B)Raffle B

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Q. There are two different raffles you can enter. In raffle A, one ticket out of 100100 will win a $370\$370 prize. The other tickets will win nothing. Each ticket costs $15\$15. Raffle B, which is for a fundraiser, has 200200 tickets. Each ticket costs $16\$16. One ticket will win a $680\$680 prize, and the remaining tickets will win nothing. Which raffle is a better deal?\newline(A)Raffle A\newline(B)Raffle B
  1. Calculate EVA for Raffle A: Calculate the expected value for Raffle A.\newlineExpected value (EVA) = (Prize amount ×\times Probability of winning) - Cost of ticket.\newlineEVA = ($370×1100\$370 \times \frac{1}{100}) - $15\$15.\newlineEVA = $3.70−$15\$3.70 - \$15.\newlineEVA = −$11.30-\$11.30.
  2. Calculate EVB for Raffle B: Calculate the expected value for Raffle B.\newlineExpected value (EVB) = (Prize amount ×\times Probability of winning) - Cost of ticket.\newlineEVB = ($680×1200\$680 \times \frac{1}{200}) - $16\$16.\newlineEVB = $3.40−$16\$3.40 - \$16.\newlineEVB = −$12.60-\$12.60.
  3. Compare EV of Raffle A and Raffle B: Compare the expected values of Raffle A and Raffle B. Since −$11.30-\$11.30 is greater than −$12.60-\$12.60, Raffle A has a less negative expected value, making it the better deal.

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