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There are two different raffles you can enter. Raffle A, which is at a carnival, has 1,0001,000 tickets. Each ticket costs $5\$5. One ticket will win a $120\$120 prize, and the remaining tickets will win nothing. Raffle B has 125125 tickets. Each ticket costs $11\$11. One ticket will win a $850\$850 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. Raffle A, which is at a carnival, has 1,0001,000 tickets. Each ticket costs $5\$5. One ticket will win a $120\$120 prize, and the remaining tickets will win nothing. Raffle B has 125125 tickets. Each ticket costs $11\$11. One ticket will win a $850\$850 prize, and the remaining tickets will win nothing. Which raffle is a better deal?\newline(A)Raffle A\newline(B)Raffle B
  1. Calculate Expected Value Raffle A: Calculate the expected value for Raffle A.\newlineExpected value = (Probability of winning×Prize value)−(Probability of losing×Cost per ticket)(\text{Probability of winning} \times \text{Prize value}) - (\text{Probability of losing} \times \text{Cost per ticket})\newlineExpected value for Raffle A = (11000×$120)−(9991000×$5)\left(\frac{1}{1000} \times \$120\right) - \left(\frac{999}{1000} \times \$5\right)
  2. Perform Calculation Raffle A: Perform the calculation for Raffle A.\newlineExpected value for Raffle A = $(0.12)\$(0.12) - $(4.995)\$(4.995)\newlineExpected value for Raffle A = −$(4.875)-\$(4.875)
  3. Calculate Expected Value Raffle B: Calculate the expected value for Raffle B.\newlineExpected value = (Probability of winning×Prize value)−(Probability of losing×Cost per ticket)(\text{Probability of winning} \times \text{Prize value}) - (\text{Probability of losing} \times \text{Cost per ticket})\newlineExpected value for Raffle B = (1125×$850)−(124125×$11)\left(\frac{1}{125} \times \$850\right) - \left(\frac{124}{125} \times \$11\right)
  4. Perform Calculation Raffle B: Perform the calculation for Raffle B.\newlineExpected value for Raffle B = ($6.80)−($11.088)(\$6.80) - (\$11.088)\newlineExpected value for Raffle B = −$4.288-\$4.288
  5. Compare Expected Values: Compare the expected values of both raffles to determine which is a better deal. Raffle A has an expected value of −$4.875-\$4.875, and Raffle B has an expected value of −$4.288-\$4.288. Since the expected value is less negative for Raffle B, it is the better deal.

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