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There are two different raffles you can enter.\newlineRaffle A, which is for a fundraiser, has 125125 tickets. Each ticket costs $7\$7. One ticket will win a $400\$400 prize, and the remaining tickets will win nothing.\newlineRaffle B has 500500 tickets. Each ticket costs $4\$4. One ticket will win a $170\$170 prize, thirteen tickets will win a $40\$40 prize, seventeen tickets 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\newline

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Q. There are two different raffles you can enter.\newlineRaffle A, which is for a fundraiser, has 125125 tickets. Each ticket costs $7\$7. One ticket will win a $400\$400 prize, and the remaining tickets will win nothing.\newlineRaffle B has 500500 tickets. Each ticket costs $4\$4. One ticket will win a $170\$170 prize, thirteen tickets will win a $40\$40 prize, seventeen tickets 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\newline
  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 = 125125 * $7\$7\newlineTotal cost for Raffle A = $875\$875
  2. Calculate Expected Value Raffle A: Calculate the expected value of a 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 = ($400−$875)/125(\$400 - \$875) / 125\newlineExpected value for Raffle A = −$3.80-\$3.80
  3. Calculate Total Cost Raffle B: Calculate the total cost of all tickets for Raffle B.\newlineTotal cost for Raffle B = Number of tickets * Cost per ticket\newlineTotal cost for Raffle B = 500500 * $4\$4\newlineTotal cost for Raffle B = $2000\$2000
  4. Calculate Total Prize Money Raffle B: Calculate the total prize money for Raffle B.\newlineTotal prize money for Raffle B = (1×$170)+(13×$40)+(17×$30)(1 \times \$170) + (13 \times \$40) + (17 \times \$30)\newlineTotal prize money for Raffle B = $170+$520+$510\$170 + \$520 + \$510\newlineTotal prize money for Raffle B = $1200\$1200
  5. Calculate Expected Value Raffle B: Calculate the expected value of a ticket in Raffle B.\newlineExpected value for Raffle B = (Prize value−Total cost)/Number of tickets(\text{Prize value} - \text{Total cost}) / \text{Number of tickets}\newlineExpected value for Raffle B = ($1200−$2000)/500(\$1200 - \$2000) / 500\newlineExpected value for Raffle B = −$1.60-\$1.60
  6. Compare Expected Values: Compare the expected values of both raffles to determine the better deal.\newlineRaffle A has an expected value of −$3.80-\$3.80 per ticket.\newlineRaffle B has an expected value of −$1.60-\$1.60 per ticket.\newlineSince the expected value is less negative for Raffle B, it is the better deal.

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