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There are two different raffles you can enter.\newlineRaffle A has 125125 tickets. Each ticket costs $15\$15. One ticket will win a $940\$940 prize, and the remaining tickets will win nothing.\newlineRaffle B has 100100 tickets. Each ticket costs $4\$4. One ticket will win a $210\$210 prize, one ticket will win a $30\$30 prize, and the remaining 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 has 125125 tickets. Each ticket costs $15\$15. One ticket will win a $940\$940 prize, and the remaining tickets will win nothing.\newlineRaffle B has 100100 tickets. Each ticket costs $4\$4. One ticket will win a $210\$210 prize, one ticket will win a $30\$30 prize, and the remaining tickets will win nothing.\newlineWhich raffle is a better deal?\newline(A)Raffle A\newline(B)Raffle B
  1. Calculate Total Cost Raffle A: Calculate the total cost for all tickets in Raffle A.\newlineTotal cost for Raffle A = Number of tickets ×\times Cost per ticket\newlineTotal cost for Raffle A = 125×$15125 \times \$15
  2. Calculate Expected Value Raffle A: Total cost for Raffle A = $1875\$1875
  3. Calculate Total Cost Raffle B: Calculate the expected value of one ticket in Raffle A.\newlineExpected value for Raffle A = (Prize value−Total cost)/Number of tickets(\text{Prize value} - \text{Total cost}) / \text{Number of tickets}\newlineExpected value for Raffle A = ($940−$1875)/125(\$940 - \$1875) / 125
  4. Calculate Expected Value Raffle B: Expected value for Raffle A = −$7.48-\$7.48
  5. Compare Expected Values: Calculate the total cost for all tickets in Raffle B.\newlineTotal cost for Raffle B = Number of tickets * Cost per ticket\newlineTotal cost for Raffle B = 100100 * $4\$4
  6. Compare Expected Values: Calculate the total cost for all tickets in Raffle B.\newlineTotal cost for Raffle B = Number of tickets * Cost per ticket\newlineTotal cost for Raffle B = \(100\) * \(\$4\)Total cost for Raffle B = \(\$400\)
  7. Compare Expected Values: Calculate the total cost for all tickets in Raffle B.\(\newline\)Total cost for Raffle B = Number of tickets * Cost per ticket\(\newline\)Total cost for Raffle B = 100100 * $4\$4Total cost for Raffle B = $400\$400Calculate the expected value of one ticket in Raffle B.\newlineExpected value for Raffle B = (Sum of prize values - Total cost) / Number of tickets\newlineExpected value for Raffle B = $$210+$30−$400\$\$210 + \$30 - \$400 / 100100\)
  8. Compare Expected Values: Calculate the total cost for all tickets in Raffle B.\newlineTotal cost for Raffle B = Number of tickets * Cost per ticket\newlineTotal cost for Raffle B = $\(100\) * \(\$4\) Total cost for Raffle B = \(\$400\) Calculate the expected value of one ticket in Raffle B.\(\newline\)Expected value for Raffle B = (Sum of prize values - Total cost) / Number of tickets\(\newline\)Expected value for Raffle B = \(\$\$210 + \$30 - \$400\) / \(100\)\) Expected value for Raffle B = \(-\$1.60\)
  9. Compare Expected Values: Calculate the total cost for all tickets in Raffle B.\(\newline\)Total cost for Raffle B = Number of tickets * Cost per ticket\(\newline\)Total cost for Raffle B = \(100 \times \$4\) Total cost for Raffle B = \(\$400\) Calculate the expected value of one ticket in Raffle B.\(\newline\)Expected value for Raffle B = (Sum of prize values - Total cost) / Number of tickets\(\newline\)Expected value for Raffle B = \((\$210 + \$30 - \$400) / 100\) Expected value for Raffle B = \(-\$1.60\) Compare the expected values of both raffles to determine the better deal.\(\newline\)Raffle B has a higher expected value \(-\$1.60\) than Raffle A \(-\$7.48\), so Raffle B is the better deal.

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