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There are two different raffles you can enter.\newlineRaffle A has 1,0001,000 tickets. Each ticket costs $9\$9. One ticket will win a $250\$250 prize, and the remaining tickets will win nothing.\newlineRaffle B has 250250 tickets, and each costs $18\$18. One ticket will win a $230\$230 prize, five tickets will win a $110\$110 prize, and seventeen tickets will win a $60\$60 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.\newlineRaffle A has 1,0001,000 tickets. Each ticket costs $9\$9. One ticket will win a $250\$250 prize, and the remaining tickets will win nothing.\newlineRaffle B has 250250 tickets, and each costs $18\$18. One ticket will win a $230\$230 prize, five tickets will win a $110\$110 prize, and seventeen tickets will win a $60\$60 prize. The remaining tickets will win nothing.\newlineWhich raffle is a better deal?\newline(A)Raffle A\newline(B)Raffle B
  1. Calculate Expected Value Raffle A: Calculate the expected value for Raffle A.\newlineE(A)=11000×$(250)+9991000×$(0)E(A) = \frac{1}{1000} \times \$(250) + \frac{999}{1000} \times \$(0)\newlineE(A)=$(0.25)E(A) = \$(0.25)
  2. Calculate Expected Profit Raffle A: Subtract the cost of one ticket from the expected value for Raffle A to find the expected profit.\newlineExpected profit A = E(A)−$9E(A) - \$9\newlineExpected profit A = $0.25−$9\$0.25 - \$9\newlineExpected profit A = −$8.75-\$8.75
  3. Calculate Expected Value Raffle B $\$230230 Prize: Calculate the expected value for Raffle B for the $\$230230 prize.E(B1)=(1250)∗$230E(B1) = \left(\frac{1}{250}\right) * \$230E(B1)=$0.92E(B1) = \$0.92
  4. Calculate Expected Value Raffle B $110\$110 Prizes: Calculate the expected value for Raffle B for the $110\$110 prizes.E(B2)=(5250)∗$110E(B2) = \left(\frac{5}{250}\right) * \$110E(B2)=$2.20E(B2) = \$2.20
  5. Calculate Expected Value Raffle B $60\$60 Prizes: Calculate the expected value for Raffle B for the $60\$60 prizes.E(B3)=(17250)∗$60E(B3) = \left(\frac{17}{250}\right) * \$60E(B3)=$4.08E(B3) = \$4.08
  6. Calculate Total Expected Value Raffle B: Add up the expected values for all prizes in Raffle B.\newlineTotal E(B)=E(B1)+E(B2)+E(B3)E(B) = E(B1) + E(B2) + E(B3)\newlineTotal E(B)=$0.92+$2.20+$4.08E(B) = \$0.92 + \$2.20 + \$4.08\newlineTotal E(B)=$7.20E(B) = \$7.20
  7. Calculate Expected Profit Raffle B: Subtract the cost of one ticket from the total expected value for Raffle B to find the expected profit.\newlineExpected profit B = Total E(B)E(B) - $18\$18\newlineExpected profit B = $7.20\$7.20 - $18\$18\newlineExpected profit B = -$10.80\$10.80

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