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There are two different raffles you can enter. Raffle A is for a $180\$180 prize. Out of 250250 tickets, each costing $15\$15, one ticket will win the prize, and the rest will win nothing. Raffle B is for a $910\$910 prize. Out of 500500 tickets, each costing $17\$17, one ticket will win the prize, and the rest will win nothing. Which 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. Raffle A is for a $180\$180 prize. Out of 250250 tickets, each costing $15\$15, one ticket will win the prize, and the rest will win nothing. Raffle B is for a $910\$910 prize. Out of 500500 tickets, each costing $17\$17, one ticket will win the prize, and the rest will win nothing. Which 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.\newlineExpected value = (Prize value×Probability of winning)−(Cost per ticket×Probability of losing)(\text{Prize value} \times \text{Probability of winning}) - (\text{Cost per ticket} \times \text{Probability of losing})\newlineExpected value for Raffle A = ($180×1250)−($15×249250)(\$180 \times \frac{1}{250}) - (\$15 \times \frac{249}{250})
  2. Perform Calculation Raffle A: Perform the calculation for Raffle A.\newlineExpected value for Raffle A = 0.720.72 - 14.8514.85\newlineExpected value for Raffle A = -$14.13\$14.13
  3. Calculate Expected Value Raffle B: Calculate the expected value for Raffle B.\newlineExpected value for Raffle B = ($910×1500)−($17×499500)(\$910 \times \frac{1}{500}) - (\$17 \times \frac{499}{500})
  4. Perform Calculation Raffle B: Perform the calculation for Raffle B.\newlineExpected value for Raffle B = (1.82)−(16.966)(1.82) - (16.966)\newlineExpected value for Raffle B = −$15.146-\$15.146
  5. Compare Expected Values: Compare the expected values of both raffles to determine which is a better deal. Raffle A has an expected value of −$14.13-\$14.13, and Raffle B has an expected value of −$15.146-\$15.146.
  6. Conclude Better Deal: Conclude which raffle offers the better deal based on the higher expected value. Raffle A is the better deal because it has a less negative expected value.

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