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There are two different raffles you can enter.\newlineRaffle A is for a $870\$870 prize. Out of 1,0001,000 tickets, each costing $6\$6, one ticket will win the prize, and the remaining tickets will win nothing.\newlineRaffle B has 200200 tickets, and each costs $12\$12. One ticket will win a $690\$690 prize, one ticket will win a $430\$430 prize, and one ticket will win a $300\$300 prize. The remaining tickets will win nothing.\newlineWhich raffle is a better deal?\newlineChoices:\newline(A)Raffle A\newline(B)Raffle B\newline

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Q. There are two different raffles you can enter.\newlineRaffle A is for a $870\$870 prize. Out of 1,0001,000 tickets, each costing $6\$6, one ticket will win the prize, and the remaining tickets will win nothing.\newlineRaffle B has 200200 tickets, and each costs $12\$12. One ticket will win a $690\$690 prize, one ticket will win a $430\$430 prize, and one ticket will win a $300\$300 prize. The remaining tickets will win nothing.\newlineWhich raffle is a better deal?\newlineChoices:\newline(A)Raffle A\newline(B)Raffle B\newline
  1. Calculate Expected Value Raffle A: Calculate the expected value for Raffle A.\newlineE(A) = (\text{Prize} \times \text{Probability of Winning}) - (\text{Cost per Ticket})\newlineE(A)=($(870)×11000)−$(6)E(A) = (\$(870) \times \frac{1}{1000}) - \$(6)\newlineE(A)=$(0.87)−$(6)E(A) = \$(0.87) - \$(6)\newlineE(A)=−$(5.13)E(A) = -\$(5.13)
  2. Calculate Expected Value Raffle B: Calculate the expected value for Raffle B.\newlineFirst, find the total prize amount.\newlineTotal Prize = $690\$690 + $430\$430 + $300\$300\newlineTotal Prize = $1420\$1420
  3. Find Total Prize Raffle B: Now, calculate the expected value for Raffle B.\newlineE(B)=(Total Prize×Probability of Winning)−(Cost per Ticket)E(B) = (\text{Total Prize} \times \text{Probability of Winning}) - (\text{Cost per Ticket})\newlineE(B)=($1420×3200)−$12E(B) = (\$1420 \times \frac{3}{200}) - \$12\newlineE(B)=($1420×0.015)−$12E(B) = (\$1420 \times 0.015) - \$12\newlineE(B)=$21.30−$12E(B) = \$21.30 - \$12\newlineE(B)=$9.30E(B) = \$9.30

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