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There are two different raffles you can enter.\newlineRaffle A, which is for a fundraiser, has 250250 tickets. Each ticket costs $11\$11. One ticket will win a $890\$890 prize, and the remaining tickets will win nothing.\newlineOut of 500500 tickets in raffle B, each costing $4\$4, one ticket will win a $270\$270 prize. The other tickets will win nothing.\newlineWhich 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.\newlineRaffle A, which is for a fundraiser, has 250250 tickets. Each ticket costs $11\$11. One ticket will win a $890\$890 prize, and the remaining tickets will win nothing.\newlineOut of 500500 tickets in raffle B, each costing $4\$4, one ticket will win a $270\$270 prize. The other tickets will win nothing.\newlineWhich 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 = (1250×$890)−(249250×$11)\left(\frac{1}{250} \times \$890\right) - \left(\frac{249}{250} \times \$11\right)
  2. Perform Calculations Raffle A: Perform the calculations for Raffle A.\newlineExpected value for Raffle A = ($3.56)−($9.90)(\$3.56) - (\$9.90)\newlineExpected value for Raffle A = −$6.34-\$6.34
  3. Calculate Expected Value Raffle B: Calculate the expected value for Raffle B. Expected value for Raffle B = 1500∗($270)\frac{1}{500} * (\$270) - 499500∗($4)\frac{499}{500} * (\$4)
  4. Perform Calculations Raffle B: Perform the calculations for Raffle B.\newlineExpected value for Raffle B = ($0.54)−($3.996)(\$0.54) - (\$3.996)\newlineExpected value for Raffle B = −$3.456-\$3.456
  5. Compare Expected Values: Compare the expected values of both raffles to determine the better deal. Raffle A has an expected value of −$6.34-\$6.34, and Raffle B has an expected value of −$3.456-\$3.456.
  6. Conclude Better Deal: Conclude which raffle is a better deal based on the higher expected value.\newlineRaffle B is a better deal because it has a less negative expected value.

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