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There are two different raffles you can enter.\newlineOut of 200200 tickets in raffle A, each costing $20\$20, one ticket will win a $880\$880 prize. The other tickets will win nothing.\newlineRaffle B has 250250 tickets, and each costs $10\$10. One ticket will win a $510\$510 prize, one ticket will win a $450\$450 prize, one ticket will win a $250\$250 prize, and one ticket will win a $30\$30 prize. The rest 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.\newlineOut of 200200 tickets in raffle A, each costing $20\$20, one ticket will win a $880\$880 prize. The other tickets will win nothing.\newlineRaffle B has 250250 tickets, and each costs $10\$10. One ticket will win a $510\$510 prize, one ticket will win a $450\$450 prize, one ticket will win a $250\$250 prize, and one ticket will win a $30\$30 prize. The rest will win nothing.\newlineWhich raffle is a better deal?\newline(A)Raffle A\newline(B)Raffle B
  1. Calculate Expected Value Raffle A: Calculate the expected value for Raffle A.\newlineExpected value = (\text{Probability of winning} \times \text{Prize value}) - (\text{Probability of losing} \times \text{Cost per ticket})\newlineExpected value for Raffle A = (1200×$(880))−(199200×$(20))\left(\frac{1}{200} \times \$(880)\right) - \left(\frac{199}{200} \times \$(20)\right)
  2. Perform Calculations Raffle A: Perform the calculations for Raffle A.\newlineExpected value for Raffle A = (4.40)−(4.40) - (1919.9090)\newlineExpected value for Raffle A = -$\(15\).\(50\)
  3. Calculate Expected Value Raffle B: Calculate the expected value for Raffle B.\(\newline\)Expected value = \((\text{Probability of winning the }\$510 \text{ prize} \times \text{Prize value}) + (\text{Probability of winning the }\$450 \text{ prize} \times \text{Prize value}) + (\text{Probability of winning the }\$250 \text{ prize} \times \text{Prize value}) + (\text{Probability of winning the }\$30 \text{ prize} \times \text{Prize value}) - (\text{Probability of losing} \times \text{Cost per ticket})\)\(\newline\)Expected value for Raffle B = \((\frac{1}{250} \times \$510) + (\frac{1}{250} \times \$450) + (\frac{1}{250} \times \$250) + (\frac{1}{250} \times \$30) - (\frac{246}{250} \times \$10)\)
  4. Perform Calculations Raffle B: Perform the calculations for Raffle B.\(\newline\)Expected value for Raffle B = \((\$2.04) + (\$1.80) + (\$1.00) + (\$0.12) - (\$9.84)\)\(\newline\)Expected value for Raffle B = \(\$5.96 - \$9.84\)\(\newline\)Expected value for Raffle B = \(-\$3.88\)

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