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There are two different raffles you can enter. Raffle A has 100100 tickets. Each ticket costs $20\$20. One ticket will win a $390\$390 prize, and the remaining tickets will win nothing. Raffle B is for a $100\$100 prize. Out of 250250 tickets, each costing $17\$17, one ticket will win the prize, and the remaining tickets 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 has 100100 tickets. Each ticket costs $20\$20. One ticket will win a $390\$390 prize, and the remaining tickets will win nothing. Raffle B is for a $100\$100 prize. Out of 250250 tickets, each costing $17\$17, one ticket will win the prize, and the remaining tickets 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 (EVA) = (Prize amount×Probability of winning)−(Ticket cost×Probability of losing)(\text{Prize amount} \times \text{Probability of winning}) - (\text{Ticket cost} \times \text{Probability of losing})\newlineEVA = ($390×1100)−($20×99100)(\$390 \times \frac{1}{100}) - (\$20 \times \frac{99}{100})\newlineEVA = $3.90−$19.80\$3.90 - \$19.80\newlineEVA = −$15.90-\$15.90
  2. Calculate Expected Value Raffle B: Calculate the expected value for Raffle B.\newlineExpected value (EVB) = (Prize amount ×\times Probability of winning) - (Ticket cost ×\times Probability of losing)\newlineEVB = ($100×1250\$100 \times \frac{1}{250}) - ($17×249250\$17 \times \frac{249}{250})\newlineEVB = $0.40\$0.40 - $16.932\$16.932\newlineEVB = −$16.532-\$16.532

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