()) There are two different raffles you can enter. ()) In raffle \( A \), one ticket will win a \( \$ 260 \) prize, one ticket will win a \( \$ 210 \) prize, one ticket will win a \( \$ 50 \) prize, and the remaining tickets will win nothing. There are 100 in the raffle, each costing \( \$ 17 \). ()) Raffle \( B \), which is for a fundraiser, has 200 tickets. Each ticket costs \( \$ 5 \). One ticket will win a \( \$ 150 \) prize, sixteen tickets will win a \( \$ 20 \) prize, and the remaining tickets will win nothing. ()) Which raffle is a better deal? Raffle A

To determine which raffle is a better deal, we need to calculate the expected value of each raffle. The expected value is the average amount of money that can be won in a raffle. For Raffle A: - There are 100 tickets in total. - The prizes are $260, $210, and $50. - The remaining tickets win nothing. Let's calculate the expected value for Raffle A: \[ \text{Expected Value} = \frac{1}{100} \times \$260 + \frac{1}{100} \times \$210 + \frac{1}{100} \times \$50 \] \[ \text{Expected Value} = \$2.60 + \$2.10 + \$0.50 \] \[ \text{Expected Value} = \$5.20 \] For Raffle B: - There are 200 tickets in total. - The prizes are $150 and $20. - The remaining tickets win nothing. Let's calculate the expected value for Raffle B: \[ \text{Expected Value} = \frac{1}{200} \times \$150 + \frac{16}{200} \times \$20 \] \[ \text{Expected Value} = \$0.75 + \$1.60 \] \[ \text{Expected Value} = \$2.35 \] Comparing the expected values, Raffle A has a higher expected value of $5.20 compared to Raffle B's expected value of $2.35. Therefore, Raffle A is a better deal.