Score: 0 of 4 points You buy a lottery ticket to a lottery that costs \( \$ 15 \) per ticket. There are only 300 tickets available to be sold in this lottery. In this lottery there are one \( \$ 500 \) prize(s), two \( \$ 100 \) prizes, and fifteen \( \$ 25 \) prizes. Find your expected gain or loss. (Round to 2 decimal places if needed.) Expected gain or loss \( \approx \$ \) Enter your answer Note: Represent a gain with a positive answer and a loss with a negative answer.
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To calculate the expected gain or loss, we first need to determine the total value of the prizes in the lottery as well as the total number of tickets sold. 1. **Total Prizes:** - One $500 prize - Two $100 prizes: \( 2 \times 100 = 200 \) - Fifteen $25 prizes: \( 15 \times 25 = 375 \) Adding these together: \[ \text{Total Prizes} = 500 + 200 + 375 = 1075 \] 2. **Total Tickets Sold:** There are 300 tickets sold at $15 each. 3. **Calculating the Expected Value:** The expected value per ticket can be calculated by dividing the total value of prizes by the number of tickets, then subtracting the ticket cost. \[ \text{Expected Value} = \frac{\text{Total Prizes}}{\text{Total Tickets}} - \text{Cost of Ticket} \] \[ \text{Expected Value} = \frac{1075}{300} - 15 \] Calculating the expected value: - First, calculate \( \frac{1075}{300} \approx 3.5833 \). - Now, subtract the cost of the ticket: \[ \text{Expected Value} \approx 3.58 - 15 = -11.42 \] Thus, your expected gain or loss is approximately: \[ \text{Expected gain or loss} \approx -11.42 \] So, you can expect a loss of about **$11.42**.