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There are two different raffles you can enter. Raffle A, which is at a carnival, has 125125 tickets. Each ticket costs $4\$4. One ticket will win a $280\$280 prize, and the remaining tickets will win nothing. Out of 5050 tickets in raffle B, each costing $15\$15, one ticket will win a $480\$480 prize, and one ticket will win a $210\$210 prize. 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 125125 tickets. Each ticket costs $4\$4. One ticket will win a $280\$280 prize, and the remaining tickets will win nothing. Out of 5050 tickets in raffle B, each costing $15\$15, one ticket will win a $480\$480 prize, and one ticket will win a $210\$210 prize. The remaining tickets will win nothing. Which raffle is a better deal?\newline(A)Raffle A\newline(B)Raffle B
  1. Calculate Total Cost Raffle A: Calculate the total cost of all tickets for Raffle A.\newlineTotal cost for Raffle A = Number of tickets * Cost per ticket\newlineTotal cost for Raffle A = \(125\) * \(\$4\)\(\newline\)Total cost for Raffle A = \(\$500\)
  2. Calculate Expected Value Raffle A: Calculate the expected value of a ticket in Raffle A.\(\newline\)Expected value for Raffle A = \((\text{Prize value} - \text{Total cost}) / \text{Number of tickets}\)\(\newline\)Expected value for Raffle A = \((\$280 - \$500) / 125\)\(\newline\)Expected value for Raffle A = \(-\$1.76\)
  3. Calculate Total Cost Raffle B: Calculate the total cost of all tickets for Raffle B.\(\newline\)Total cost for Raffle B = Number of tickets * Cost per ticket\(\newline\)Total cost for Raffle B = 5050 * $15\$15\newlineTotal cost for Raffle B = $750\$750
  4. Calculate Expected Value Raffle B: Calculate the expected value of a ticket in Raffle B.\newlineExpected value for Raffle B = (Total prize value−Total cost)/Number of tickets(\text{Total prize value} - \text{Total cost}) / \text{Number of tickets}\newlineExpected value for Raffle B = ($(480)+$(210)−$(750))/50(\$(480) + \$(210) - \$(750)) / 50\newlineExpected value for Raffle B = −$(1.20)-\$(1.20)
  5. Compare Expected Values: Compare the expected values of both raffles to determine the better deal. Raffle A has an expected value of −$1.76-\$1.76 per ticket, and Raffle B has an expected value of −$1.20-\$1.20 per ticket. Since the expected value is less negative for Raffle B, it is the better deal.

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