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It seems the problem involves finding the expected value of a raffle with 2400 tickets sold for $10 each and a cash prize of $4800. The expected value is the average gain or loss per ticket for someone participating in the raffle.

Let’s calculate the expected value step by step.

1. **Total Number of Tickets Sold:** 2400 tickets
2. **Cost per Ticket:** $10
3. **Cash Prize:** $4800

The formula for expected value $E(X)$ in a raffle is:

\[
E(X) = \left(\frac{\text{prize}}{\text{total tickets}}\right) \times \text{probability of winning} + \left(\text{cost of losing}\right) \times \text{probability of losing}
\]

In this case:
- The probability of winning $ = \frac{1}{2400} $.
- The probability of losing $ = \frac{2399}{2400} $.
- The gain from winning is $4800, but we need to subtract the $10 cost of the ticket, so the net gain is $4790.
- The loss from losing is just the cost of the ticket, which is $10.

Now, calculate:

\[
E(X) = \left(4790 \times \frac{1}{2400}\right) + \left(-10 \times \frac{2399}{2400}\right)
\]

1. $ 4790 \times \frac{1}{2400} = 1.9958333 $ (approximately $2)
2. $ -10 \times \frac{2399}{2400} = -9.9958333 $ (approximately -$10)

Now summing these:

\[
E(X) = 1.9958333 - 9.9958333 = -8
\]

So, the expected value is **-8 dollars**, which matches the correct answer shown in your image.

Would you like a more detailed breakdown, or do you have any specific questions about this?

Here are 5 related questions for further exploration:
1. How would the expected value change if the prize amount was higher?
2. What would the expected value be if the number of tickets sold doubled?
3. How can the expected value formula be applied to other types of games, like lotteries?
4. What is the significance of a negative expected value in a raffle or lottery context?
5. How would the expected value change if multiple prizes were awarded?

**Tip:** In situations involving expected value, a negative value indicates an average loss, meaning that over many trials, participants would expect to lose money on average.

A cash prize of $4800 is to be awarded at a fundraiser. If 2400 tickets are sold at $10 each, find the expected value.

Calculate the expected value for a raffle with a $4800 prize and 2400 tickets sold at $10 each. This problem covers key concepts in probability and expected value, suitable for high school students in Grades 9-12.

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