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There are two different raffles you can enter.\newlineRaffle A is for a $750\$750 prize. Out of 200200 tickets, each costing $19\$19, one ticket will win the prize, and the rest will win nothing.\newlineRaffle B is for a $170\$170 prize. Out of 250250 tickets, each costing $16\$16, one ticket will win the prize, and the remaining 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 is for a $750\$750 prize. Out of 200200 tickets, each costing $19\$19, one ticket will win the prize, and the rest will win nothing.\newlineRaffle B is for a $170\$170 prize. Out of 250250 tickets, each costing $16\$16, one ticket will win the prize, and the remaining tickets will win nothing.\newlineWhich raffle is a better deal?\newline(A) Raffle A\newline(B) Raffle B
  1. Calculate Expected Value Raffle A: Calculate the expected value for Raffle A.\newlineE(A) = (\text{Prize value} \times \text{Probability of winning}) - (\text{Cost per ticket})\newlineE(A)=($750×1200)−$19E(A) = (\$750 \times \frac{1}{200}) - \$19\newlineE(A)=$3.75−$19E(A) = \$3.75 - \$19\newlineE(A)=−$15.25E(A) = -\$15.25
  2. Calculate Expected Value Raffle B: Calculate the expected value for Raffle B.\newlineE(B)=(Prize value×Probability of winning)−(Cost per ticket)E(B) = (\text{Prize value} \times \text{Probability of winning}) - (\text{Cost per ticket})\newlineE(B)=($(170)×1250)−$(16)E(B) = (\$(170) \times \frac{1}{250}) - \$(16)\newlineE(B)=$(0.68)−$(16)E(B) = \$(0.68) - \$(16)\newlineE(B)=−$(15.32)E(B) = -\$(15.32)
  3. Compare Expected Values: Compare the expected values of Raffle A and Raffle B.\newlineSince −$15.25-\$15.25 is greater than −$15.32-\$15.32, Raffle A has a less negative expected value, making it the better deal.

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