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There are two different raffles you can enter. In raffle A, one ticket will win a $720\$720 prize, and the remaining tickets will win nothing. There are 250250 in the raffle, each costing $20\$20. In raffle B, one ticket will win a $260\$260 prize, one ticket will win a $200\$200 prize, and the remaining tickets will win nothing. There are 100100 in the raffle, each costing $3\$3. 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. In raffle A, one ticket will win a $720\$720 prize, and the remaining tickets will win nothing. There are 250250 in the raffle, each costing $20\$20. In raffle B, one ticket will win a $260\$260 prize, one ticket will win a $200\$200 prize, and the remaining tickets will win nothing. There are 100100 in the raffle, each costing $3\$3. Which raffle is a better deal?\newline(A)Raffle A\newline(B)Raffle B
  1. Calculate Expected Value Raffle A: Calculate the expected value for Raffle A.\newlineExpected value = (Probability of winning×Prize value)−(Probability of losing×Cost per ticket)(\text{Probability of winning} \times \text{Prize value}) - (\text{Probability of losing} \times \text{Cost per ticket})\newline= (1250×$(720))−(249250×$(20))\left(\frac{1}{250} \times \$(720)\right) - \left(\frac{249}{250} \times \$(20)\right)
  2. Math Raffle A: Do the math for Raffle A.\newlineExpected value = (2.88)−(2.88) - (1919.8080)\newline= -\(16\).\(92\)
  3. Calculate Expected Value Raffle B: Calculate the expected value for Raffle B.\(\newline\)Expected value = (Probability of winning the \(\$\)\(260\) prize \(*\) Prize value) + (Probability of winning the \(\$\)\(200\) prize \(*\) Prize value) - (Probability of losing \(*\) Cost per ticket)\(\newline\)= \((\frac{\(1\)}{\(100\)} \(*\) \(\$\)\(260\)) + (\frac{\(1\)}{\(100\)} \(*\) \(\$\)\(200\)) - (\frac{\(98\)}{\(100\)} \(*\) \(\$\)\(3\))\)
  4. Math Raffle B: Do the math for Raffle B.\(\newline\)Expected value = (\(2.60) + (\)\(2\).\(00\)) - (22.9494)\newline= $\(1\).\(66\)

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