Question 4, 11.5.15 HW Score: $34.38 \%, 2.75$ of Part 2 of 3 8 points rk 11.5 ( Points: 0 of 1 Save A college foundation raises funds by selling 600 raffle tickets for a new car worth $\$ 37,000$ at $\$ 100$ each. (a) Find the expected net winnings of a person buying one of the tickets. (b) Find the total profit for the foundation, assuming they had to purchase the car. (c) Find the total profit for the foundation, assuming the car was donated. (a) The expected net winnings are $\$-38.33$. (Round to the nearest hundredth as needed.) (b) Assuming they had to purchase the car, the total profit for the foundation is $\$ \square$. (Simplify your answer.)

Step 1 ：Calculate the expected net winnings of a person buying one of the tickets. The probability of winning the car is \(\frac{1}{600}\). If a person wins, their net winnings would be the value of the car minus the cost of the ticket, which is \($37,000 - $100 = $36,900\). If a person loses, their net winnings would be -$100 (the cost of the ticket).

Step 2 ：So, the expected net winnings would be \(\left(\frac{1}{600} \times $36,900\right) + \left(\frac{599}{600} \times -$100\right) = $-38.33\) (rounded to the nearest hundredth).

Step 3 ：If the foundation had to purchase the car, the total profit would be the total revenue from selling the tickets minus the cost of the car. The total revenue from selling the tickets is \(600 \times $100 = $60,000\).

Step 4 ：So, the total profit would be \($60,000 - $37,000 = $23,000\).

Step 5 ：If the car was donated, the total profit for the foundation would be just the total revenue from selling the tickets, which is \(\boxed{$60,000}\).