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There are two different raffles you can enter. Raffle A has 5050 tickets. Each ticket costs $5\$5. One ticket will win a $190\$190 prize, and the remaining tickets will win nothing. In raffle B, one ticket out of 1,0001,000 will win a $690\$690 prize, and twelve tickets will win a $650\$650 prize. The rest will win nothing. Each ticket costs $9\$9. 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 5050 tickets. Each ticket costs $5\$5. One ticket will win a $190\$190 prize, and the remaining tickets will win nothing. In raffle B, one ticket out of 1,0001,000 will win a $690\$690 prize, and twelve tickets will win a $650\$650 prize. The rest will win nothing. Each ticket costs $9\$9. Which raffle is a better deal?\newline(A)Raffle A\newline(B)Raffle B
  1. Calculate EVA for Raffle A: Calculate the expected value for Raffle A.\newlineExpected value (EVA) = (Probability of winning ×\times Prize value) + (Probability of not winning ×\times 00)\newlineEVA = (150\frac{1}{50} ×\times $190\$190) + (4950\frac{49}{50} ×\times $0\$0)\newlineEVA = $3.80\$3.80 + $0\$0\newlineEVA = $3.80\$3.80
  2. Subtract cost for expected profit A: Subtract the cost of one ticket from the expected value to find the expected profit for Raffle A.\newlineExpected profit (EPA) = Expected value - Cost per ticket\newlineEPA=$3.80−$5EPA = \$3.80 - \$5\newlineEPA=−$1.20EPA = -\$1.20
  3. Calculate EVB for Raffle B: Calculate the expected value for Raffle B.\newlineExpected value (EVB) = (Probability of winning the $\$690690 prize ×\times Prize value) + (Probability of winning the $\$650650 prize ×\times Prize value) + (Probability of not winning ×\times 00)\newlineEVB = 11000×$690\frac{1}{1000} \times \$690 + 121000×$650\frac{12}{1000} \times \$650 + 9871000×$0\frac{987}{1000} \times \$0\newlineEVB = \$\(0\).\(69\) + \$\(7\).\(80\)\(\newline\)EVB = \$\(8\).\(49\)
  4. Subtract cost for expected profit B: Subtract the cost of one ticket from the expected value to find the expected profit for Raffle B.\(\newline\)Expected profit (EPB) = Expected value - Cost per ticket\(\newline\)\(EPB = \$8.49 - \$9\)\(\newline\)\(EPB = -\$0.51\)
  5. Compare expected profits: Compare the expected profits of Raffle A and Raffle B to determine which is the better deal.\(\newline\)Since \(-\$1.20 < -\$0.51\), Raffle B is the better deal.

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