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There are two different raffles you can enter. Raffle A is for a $120\$120 prize. Out of 5050 tickets, each costing $20\$20, one ticket will win the prize, and the remaining tickets will win nothing. In raffle B, one ticket out of 125125 will win a $130\$130 prize, one ticket will win a $70\$70 prize, one ticket will win a $20\$20 prize, and one ticket will win a $20\$20 prize. The remaining tickets will win nothing. Each ticket costs $5\$5. Which raffle is a better deal?\newline(A)Raffle A\newline(B)Raffle B\newline

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Q. There are two different raffles you can enter. Raffle A is for a $120\$120 prize. Out of 5050 tickets, each costing $20\$20, one ticket will win the prize, and the remaining tickets will win nothing. In raffle B, one ticket out of 125125 will win a $130\$130 prize, one ticket will win a $70\$70 prize, one ticket will win a $20\$20 prize, and one ticket will win a $20\$20 prize. The remaining tickets will win nothing. Each ticket costs $5\$5. Which raffle is a better deal?\newline(A)Raffle A\newline(B)Raffle B\newline
  1. Calculate Expected Value Raffle A: Calculate the expected value for Raffle A.\newlineE(A)=(Prize×Probability of winning)−(Cost per ticket)E(A) = (\text{Prize} \times \text{Probability of winning}) - (\text{Cost per ticket})\newlineE(A)=($(120)×150)−$(20)E(A) = (\$(120) \times \frac{1}{50}) - \$(20)\newlineE(A)=$(2.40)−$(20)E(A) = \$(2.40) - \$(20)\newlineE(A)=−$(17.60)E(A) = -\$(17.60)
  2. Calculate Expected Value Raffle B: Calculate the expected value for Raffle B.\newlineFirst, find the total prize value by adding all the prizes together.\newlineTotal prize value = $130+$70+$20+$20\$130 + \$70 + \$20 + \$20\newlineTotal prize value = $240\$240\newlineNext, calculate the expected value.\newlineE(B)=(Total prize value×Probability of winning any prize)−(Cost per ticket)E(B) = (\text{Total prize value} \times \text{Probability of winning any prize}) - (\text{Cost per ticket})\newlineE(B)=($240×4125)−$5E(B) = (\$240 \times \frac{4}{125}) - \$5\newlineE(B)=($240×0.032)−$5E(B) = (\$240 \times 0.032) - \$5\newlineE(B)=$7.68−$5E(B) = \$7.68 - \$5\newlineE(B)=$2.68E(B) = \$2.68
  3. Compare Expected Values: Compare the expected values of Raffle A and Raffle B to determine which is a better deal.\newlineRaffle A has an expected value of −$17.60-\$17.60.\newlineRaffle B has an expected value of $2.68\$2.68.\newlineSince $2.68\$2.68 is greater than −$17.60-\$17.60, Raffle B is the better deal.

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