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There are two different raffles you can enter.\newlineRaffle A is for a $130\$130 prize. Out of 200200 tickets, each costing $1\$1, one ticket will win the prize, and the other tickets will win nothing.\newlineIn raffle B, one ticket out of 100100 will win a $550\$550 prize. The other tickets will win nothing. Each ticket costs $7\$7.\newlineWhich raffle is a better deal?\newlineChoices:\newline(A)Raffle A\newline(B)Raffle B

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Q. There are two different raffles you can enter.\newlineRaffle A is for a $130\$130 prize. Out of 200200 tickets, each costing $1\$1, one ticket will win the prize, and the other tickets will win nothing.\newlineIn raffle B, one ticket out of 100100 will win a $550\$550 prize. The other tickets will win nothing. Each ticket costs $7\$7.\newlineWhich raffle is a better deal?\newlineChoices:\newline(A)Raffle A\newline(B)Raffle B
  1. Calculate Expected Value: Calculate the expected value for Raffle A.\newlineE(A)=(Prize amount×Probability of winning)+(0×Probability of losing)E(A) = (\text{Prize amount} \times \text{Probability of winning}) + (0 \times \text{Probability of losing})\newlineE(A)=($(130)×1200)+($(0)×199200)E(A) = (\$(130) \times \frac{1}{200}) + (\$(0) \times \frac{199}{200})\newlineE(A)=$0.65+$0E(A) = \$0.65 + \$0\newlineE(A)=$0.65E(A) = \$0.65
  2. Find Expected Profit: Subtract the cost of one ticket from the expected value of Raffle A to find the expected profit.\newlineExpected profit A = E(A)−Cost per ticketE(A) - \text{Cost per ticket}\newlineExpected profit A = (0.65)−(1)(0.65) - (1)\newlineExpected profit A = −(0.35)-(0.35)
  3. Calculate Expected Value: Calculate the expected value for Raffle B. \newlineE(B)=(Prize amount×Probability of winning)+(0×Probability of losing)E(B) = (\text{Prize amount} \times \text{Probability of winning}) + (0 \times \text{Probability of losing})\newlineE(B)=($(550)×1100)+($(0)×99100)E(B) = (\$(550) \times \frac{1}{100}) + (\$(0) \times \frac{99}{100})\newlineE(B)=$(5.50)+$(0)E(B) = \$(5.50) + \$(0)\newlineE(B)=$(5.50)E(B) = \$(5.50)
  4. Find Expected Profit: Subtract the cost of one ticket from the expected value of Raffle B to find the expected profit.\newlineExpected profit B = E(B)−Cost per ticketE(B) - \text{Cost per ticket}\newlineExpected profit B = ($5.50)−($7)(\$5.50) - (\$7)\newlineExpected profit B = −($1.50)-(\$1.50)
  5. Compare Expected Profits: Compare the expected profits of Raffle A and Raffle B to determine which is the better deal.\newlineSince −$0.35-\$0.35 is greater than −$1.50-\$1.50, Raffle A is the better deal.

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