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There are two different raffles you can enter.\newlineOut of 250250 tickets in raffle A, each costing $7\$7, one ticket will win a $460\$460 prize. The remaining tickets will win nothing.\newlineRaffle B has 5050 tickets, and each costs $14\$14. One ticket will win a $790\$790 prize, one ticket will win a $760\$760 prize, one ticket will win a $710\$710 prize, and one ticket will win a $20\$20 prize. The remaining 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.\newlineOut of 250250 tickets in raffle A, each costing $7\$7, one ticket will win a $460\$460 prize. The remaining tickets will win nothing.\newlineRaffle B has 5050 tickets, and each costs $14\$14. One ticket will win a $790\$790 prize, one ticket will win a $760\$760 prize, one ticket will win a $710\$710 prize, and one ticket will win a $20\$20 prize. The remaining tickets will win nothing.\newlineWhich raffle is a better deal?\newline(A)Raffle A\newline(B)Raffle B
  1. Calculate Expected Value Raffle A: Calculate the expected value for Raffle A.\newlineExpected value = (\text{Probability of winning} \times \text{Prize value}) - (\text{Probability of losing} \times \text{Cost per ticket})\newlineExpected value for Raffle A = (1250×$(460))−(249250×$(7))\left(\frac{1}{250} \times \$(460)\right) - \left(\frac{249}{250} \times \$(7)\right)
  2. Perform Calculations Raffle A: Perform the calculations for Raffle A.\newlineExpected value for Raffle A = ($1.84)−($6.972)(\$1.84) - (\$6.972)\newlineExpected value for Raffle A = −$5.132-\$5.132
  3. Calculate Expected Value Raffle B: Calculate the expected value for Raffle B.\newlineExpected value for Raffle B = (Probability of winning the $\$790790 prize ∗* Prize value) + (Probability of winning the $\$760760 prize ∗* Prize value) + (Probability of winning the $\$710710 prize ∗* Prize value) + (Probability of winning the $\$2020 prize ∗* Prize value) - (Probability of losing ∗* Cost per ticket)\newlineExpected value for Raffle B = (\frac{\(1\)}{\(50\)} \(* \$\(790\)) + (\frac{\(1\)}{\(50\)} \(*\) \$\(760\)) + (\frac{\(1\)}{\(50\)} \(*\) \$\(710\)) + (\frac{\(1\)}{\(50\)} \(*\) \$\(20\)) - (\frac{\(46\)}{\(50\)} \(*\) \$\(14\))\)
  4. Perform Calculations Raffle B: Perform the calculations for Raffle B.\(\newline\)Expected value for Raffle B = \((\$15.8 + \$15.2 + \$14.2 + \$0.4) - (\$13.16)\)\(\newline\)Expected value for Raffle B = \(\$45.6 - \$13.16\)\(\newline\)Expected value for Raffle B = \(\$32.44\)

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