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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 $410\$410 prize, and the remaining tickets will win nothing. Raffle B is for a $280\$280 prize. Out of 250250 tickets, each costing $16\$16, 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 $410\$410 prize, and the remaining tickets will win nothing. Raffle B is for a $280\$280 prize. Out of 250250 tickets, each costing $16\$16, 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×$410)−(9991000×$11)\left(\frac{1}{1000} \times \$410\right) - \left(\frac{999}{1000} \times \$11\right)
  2. Perform Calculations Raffle A: Perform the calculations for Raffle A.\newlineExpected value for Raffle A = \$\(0.4141) - \$\(10.989989)(\newline\)Expected value for Raffle A = -\$\(10.579579)
  3. Calculate Expected Value Raffle B: Calculate the expected value for Raffle B. Expected value for Raffle B = 1250∗($280)\frac{1}{250} * (\$280) - 249250∗($16)\frac{249}{250} * (\$16)
  4. Perform Calculations Raffle B: Perform the calculations for Raffle B.\newlineExpected value for Raffle B = ($1.12)−($15.84)(\$1.12) - (\$15.84)\newlineExpected value for Raffle B = −$14.72-\$14.72
  5. Compare Expected Values: Compare the expected values of both raffles to determine which is a better deal.\newlineRaffle A has an expected value of −$10.579-\$10.579 and Raffle B has an expected value of −$14.72-\$14.72.
  6. Conclude Better Deal: Conclude which raffle offers the better deal based on the higher expected value. Raffle A is the better deal because it has a less negative expected value.

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