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There are two different raffles you can enter.\newlineRaffle A has 500500 tickets. Each ticket costs $7\$7. One ticket will win a $220\$220 prize, and the remaining tickets will win nothing.\newlineRaffle B has 250250 tickets, and each costs $13\$13. One ticket will win a $370\$370 prize, six tickets will win a $260\$260 prize, and seventeen tickets will win a $50\$50 prize. The other 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 500500 tickets. Each ticket costs $7\$7. One ticket will win a $220\$220 prize, and the remaining tickets will win nothing.\newlineRaffle B has 250250 tickets, and each costs $13\$13. One ticket will win a $370\$370 prize, six tickets will win a $260\$260 prize, and seventeen tickets will win a $50\$50 prize. The other tickets will win nothing.\newlineWhich raffle is a better deal?\newline(A)Raffle A\newline(B)Raffle B
  1. Calculate Total Cost Raffle A: Calculate the total cost for all tickets in Raffle A: 500500 tickets * $7\$7 per ticket.\newline500×7=$3500500 \times 7 = \$3500.
  2. Calculate Expected Value Raffle A: Calculate the expected value for Raffle A by subtracting the prize from the total cost: $3500−$220\$3500 - \$220.3500−220=$32803500 - 220 = \$3280.
  3. Calculate Total Cost Raffle B: Calculate the total cost for all tickets in Raffle B: 250250 tickets * $13\$13 per ticket.\newline250×13=$3250250 \times 13 = \$3250.
  4. Calculate Total Prize Money Raffle B: Calculate the total prize money for Raffle B: $370\$370 for one ticket, $260\$260 for six tickets, and $50\$50 for seventeen tickets.370+(260×6)+(50×17)=$370+$1560+$850.370 + (260 \times 6) + (50 \times 17) = \$370 + \$1560 + \$850.370+1560+850=$2780.370 + 1560 + 850 = \$2780.
  5. Calculate Expected Value Raffle B: Calculate the expected value for Raffle B by subtracting the total prize money from the total cost: $3250−$2780\$3250 - \$2780.3250−2780=$4703250 - 2780 = \$470.
  6. Compare Expected Values: Compare the expected values of both raffles to determine which is a better deal. The raffle with the lower expected value is the better deal.\newlineRaffle A expected value: $3280\$3280.\newlineRaffle B expected value: $470\$470.
  7. Identify Better Deal: Since Raffle BB has a lower expected value, it is the better deal.

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