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There are two different raffles you can enter.\newlineRaffle A, which is for a fundraiser, has 200200 tickets. Each ticket costs $6\$6. One ticket will win a $920\$920 prize, and the remaining tickets will win nothing.\newlineIn raffle B, one ticket out of 200200 will win a $940\$940 prize, one ticket will win a $760\$760 prize, and one ticket will win a $340\$340 prize. The remaining tickets will win nothing. Each ticket costs $19\$19.\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, which is for a fundraiser, has 200200 tickets. Each ticket costs $6\$6. One ticket will win a $920\$920 prize, and the remaining tickets will win nothing.\newlineIn raffle B, one ticket out of 200200 will win a $940\$940 prize, one ticket will win a $760\$760 prize, and one ticket will win a $340\$340 prize. The remaining tickets will win nothing. Each ticket costs $19\$19.\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{Cost of ticket})\newlineExpected value for Raffle A = (1200×($920))−($6)\left(\frac{1}{200} \times (\$920)\right) - (\$6)
  2. Perform Calculation Raffle A: Perform the calculation for Raffle A.\newlineExpected value for Raffle A = ($920/200)−$6(\$920 / 200) - \$6\newlineExpected value for Raffle A = $4.60−$6\$4.60 - \$6\newlineExpected value for Raffle A = −$1.40-\$1.40
  3. Calculate Expected Value Raffle B: Calculate the expected value for Raffle B.\newlineExpected value = (Probability of winning the $940 prize×Prize value)+(Probability of winning the $760 prize×Prize value)+(Probability of winning the $340 prize×Prize value)−(Cost of ticket)(\text{Probability of winning the }\$940\text{ prize} \times \text{Prize value}) + (\text{Probability of winning the }\$760\text{ prize} \times \text{Prize value}) + (\text{Probability of winning the }\$340\text{ prize} \times \text{Prize value}) - (\text{Cost of ticket})\newlineExpected value for Raffle B = (1200×$940)+(1200×$760)+(1200×$340)−$19\left(\frac{1}{200} \times \$940\right) + \left(\frac{1}{200} \times \$760\right) + \left(\frac{1}{200} \times \$340\right) - \$19
  4. Perform Calculation Raffle B: Perform the calculation for Raffle B.\newlineExpected value for Raffle B = ($940/200)+($760/200)+($340/200)−$19(\$940 / 200) + (\$760 / 200) + (\$340 / 200) - \$19\newlineExpected value for Raffle B = $4.70+$3.80+$1.70−$19\$4.70 + \$3.80 + \$1.70 - \$19\newlineExpected value for Raffle B = $10.20−$19\$10.20 - \$19\newlineExpected value for Raffle B = −$8.80-\$8.80

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