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There are two different raffles you can enter. Raffle A has 1,0001,000 tickets. Each ticket costs $11\$11. One ticket will win a $880\$880 prize, and the remaining tickets will win nothing. Raffle B is for a $350\$350 prize. Out of 5050 tickets, each costing $10\$10, one ticket will win the 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 has 1,0001,000 tickets. Each ticket costs $11\$11. One ticket will win a $880\$880 prize, and the remaining tickets will win nothing. Raffle B is for a $350\$350 prize. Out of 5050 tickets, each costing $10\$10, one ticket will win the 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×$880)−(9991000×$11)\left(\frac{1}{1000} \times \$880\right) - \left(\frac{999}{1000} \times \$11\right)
  2. Perform Calculation Raffle A: Perform the calculation for Raffle A.\newlineExpected value for Raffle A = ($0.88)−($10.989)(\$0.88) - (\$10.989)\newlineExpected value for Raffle A = −$10.109-\$10.109
  3. Calculate Expected Value Raffle B: Calculate the expected value for Raffle B.\newlineExpected value = (Probability of winning×Prize value)−(Probability of losing×Cost per ticket)(\text{Probability of winning} \times \text{Prize value}) - (\text{Probability of losing} \times \text{Cost per ticket})\newlineExpected value for Raffle B = (150×$(350))−(4950×$(10))\left(\frac{1}{50} \times \$(350)\right) - \left(\frac{49}{50} \times \$(10)\right)
  4. Perform Calculation Raffle B: Perform the calculation for Raffle B.\newlineExpected value for Raffle B = (7)−(7) - (99.88)\newlineExpected value for Raffle B = -$\(2\).\(8\)
  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 \(-\$(10.109)\) and Raffle B has an expected value of \(-\$(2.8)\).
  6. Conclude Better Deal: Conclude which raffle is a better deal based on the higher expected value. Since Raffle B has a less negative expected value, it is the better deal.

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