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There are two different raffles you can enter.\newlineRaffle A has 250250 tickets. Each ticket costs $20\$20. One ticket will win a $610\$610 prize, and the remaining tickets will win nothing.\newlineIn raffle B, one ticket out of 200200 will win a $630\$630 prize, and one ticket will win a $50\$50 prize. The remaining tickets will win nothing. Each ticket costs $17\$17.\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 250250 tickets. Each ticket costs $20\$20. One ticket will win a $610\$610 prize, and the remaining tickets will win nothing.\newlineIn raffle B, one ticket out of 200200 will win a $630\$630 prize, and one ticket will win a $50\$50 prize. The remaining tickets will win nothing. Each ticket costs $17\$17.\newlineWhich 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 = (\text{Probability of winning} \times \text{Prize value}) - (\text{Ticket cost})\newlineFor Raffle A, the probability of winning is 1250\frac{1}{250}, and the prize is $610\$610.\newlineExpected value for Raffle A = (1250×$610)−$20\left(\frac{1}{250} \times \$610\right) - \$20
  2. Perform Calculation Raffle A: Perform the calculation for Raffle A.\newlineExpected value for Raffle A = \frac{\(1\)}{\(250\)} * (\$)\(610) - (\$)\(20\)(\newline\)Expected value for Raffle A = (\$)\(2\).\(44\) - (\$)\(20\)\(\newline\)Expected value for Raffle A = -(\$)\(17\).\(56\)
  3. Calculate Expected Value Raffle B: Calculate the expected value for Raffle B. There are two prizes, so we need to calculate the expected value for each prize and then add them together. For the \(\$630\) prize, the probability of winning is \(\frac{1}{200}\). For the \(\$50\) prize, the probability of winning is also \(\frac{1}{200}\). Expected value for Raffle B = \(\left(\frac{1}{200} \times \$630 + \frac{1}{200} \times \$50\right) - \$17\)
  4. Perform Calculation Raffle B: Perform the calculation for Raffle B.\(\newline\)Expected value for Raffle B = \(\frac{\(1\)}{\(200\)} * (\$)\(630\) + \frac{\(1\)}{\(200\)} * (\$)\(50\)) - (\$)\(17\)(\newline\)Expected value for Raffle B = \((\$)\(3\).\(15\) + (\$)\(0\).\(25\)) - (\$)\(17\)(\newline\)Expected value for Raffle B = (\$)\(3\).\(40\) - (\$)\(17\)(\newline\)Expected value for Raffle B = -(\$)\(13\).\(60\)
  5. Compare Expected Values: Compare the expected values of Raffle A and Raffle B to determine the better deal.\(\newline\)Raffle A has an expected value of \(-\$17.56\).\(\newline\)Raffle B has an expected value of \(-\$13.60\).\(\newline\)Since the expected value is less negative for Raffle B, it is the better deal.

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