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There are two different raffles you can enter. In raffle A, one ticket will win a $540\$540 prize, and the other tickets will win nothing. There are 125125 in the raffle, each costing $12\$12. Out of 125125 tickets in raffle B, each costing $2\$2, one ticket will win a $470\$470 prize. The rest will win nothing. Which 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. In raffle A, one ticket will win a $540\$540 prize, and the other tickets will win nothing. There are 125125 in the raffle, each costing $12\$12. Out of 125125 tickets in raffle B, each costing $2\$2, one ticket will win a $470\$470 prize. The rest will win nothing. Which raffle is a better deal?\newlineChoices:\newline(A)Raffle A\newline(B)Raffle B
  1. Calculate total cost Raffle A: Calculate the total cost of all tickets in Raffle A.\newlineTotal cost in Raffle A = Number of tickets * Cost per ticket\newlineTotal cost in Raffle A = \(125\) \times \$(\(12\))\(\newline\)Total cost in Raffle A = \$(\(1500\))
  2. Calculate expected value Raffle A: Calculate the expected value of one ticket in Raffle A.\(\newline\)Expected value of one ticket in Raffle A = Prize value / Number of tickets\(\newline\)Expected value of one ticket in Raffle A = \(\$540 / 125\)\(\newline\)Expected value of one ticket in Raffle A = \(\$4.32\)
  3. Calculate total cost Raffle B: Calculate the total cost of all tickets in Raffle B.\(\newline\)Total cost in Raffle B = Number of tickets * Cost per ticket\(\newline\)Total cost in Raffle B = 125125 * (\$)\(2\)\(\newline\)Total cost in Raffle B = (\$)\(250\)
  4. Calculate expected value Raffle B: Calculate the expected value of one ticket in Raffle B.\(\newline\)Expected value of one ticket in Raffle B = Prize value / Number of tickets\(\newline\)Expected value of one ticket in Raffle B = \(\$470 / 125\)\(\newline\)Expected value of one ticket in Raffle B = \(\$3.76\)
  5. Compare expected values: Compare the expected values of both raffles to determine the better deal.\(\newline\)Since \(\$4.32\) (Raffle A) is greater than \(\$3.76\) (Raffle B), Raffle A offers a better expected value per ticket.

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