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There are two different raffles you can enter.\newlineRaffle A, which is at a carnival, has 100100 tickets. Each ticket costs $15\$15. One ticket will win a $620\$620 prize, and the remaining tickets will win nothing.\newlineRaffle B is for a $440\$440 prize. Out of 200200 tickets, each costing $7\$7, one ticket will win the prize, and the other tickets will win nothing.\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 at a carnival, has 100100 tickets. Each ticket costs $15\$15. One ticket will win a $620\$620 prize, and the remaining tickets will win nothing.\newlineRaffle B is for a $440\$440 prize. Out of 200200 tickets, each costing $7\$7, one ticket will win the prize, and the other tickets will win nothing.\newlineWhich raffle is a better deal?\newline(A)Raffle A\newline(B)Raffle B
  1. Calculate Expected Value Raffle A: Calculate the expected value for Raffle A.\newlineExpected value = (\text{Probability of winning} \times \text{Prize value}) - (\text{Probability of losing} \times \text{Cost per ticket})\newlineFor Raffle A, the probability of winning is 1100\frac{1}{100} and the probability of losing is 99100\frac{99}{100}.\newlineExpected value for Raffle A = (1100×$(620))−(99100×$(15))\left(\frac{1}{100} \times \$(620)\right) - \left(\frac{99}{100} \times \$(15)\right)
  2. Perform Calculation Raffle A: Perform the calculation for Raffle A.\newlineExpected value for Raffle A = ($6.20)−($14.85)(\$6.20) - (\$14.85)\newlineExpected value for Raffle A = −$8.65-\$8.65
  3. Calculate Expected Value Raffle B: Calculate the expected value for Raffle B.\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})\newlineFor Raffle B, the probability of winning is 1200\frac{1}{200} and the probability of losing is 199200\frac{199}{200}.\newlineExpected value for Raffle B = (1200×($440))−(199200×($7))\left(\frac{1}{200} \times (\$440)\right) - \left(\frac{199}{200} \times (\$7)\right)
  4. Perform Calculation Raffle B: Perform the calculation for Raffle B.\newlineExpected value for Raffle B = ($2.20)−($6.965)(\$2.20) - (\$6.965)\newlineExpected value for Raffle B = −$4.765-\$4.765

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