To calculate the expected value of one raffle ticket, we'll consider both the probability of winning each prize and the probability of not winning anything.

Step 1: Calculate the probability of winning each prize.

• Total number of tickets: 10,000
• Prize 1 value: $4,800 (1 ticket wins)
• Prize 2 value: $1,200 (1 ticket wins)
• Prize 3 value: $400 (1 ticket wins)

Probability of winning each prize:

• Probability of winning the $4,800 prize: $\frac{1}{10{,}000}$
• Probability of winning the $1,200 prize: $\frac{1}{10{,}000}$
• Probability of winning the $400 prize: $\frac{1}{10{,}000}$

Step 2: Calculate the expected value from each prize.

• Expected value from Prize 1: $\frac{1}{10{,}000} \times 4{,}800 = 0.48$
• Expected value from Prize 2: $\frac{1}{10{,}000} \times 1{,}200 = 0.12$
• Expected value from Prize 3: $\frac{1}{10{,}000} \times 400 = 0.04$

Step 3: Calculate the total expected value of winning.

• Total expected value of winning: $0.48 + 0.12 + 0.04 = 0.64$

Step 4: Calculate the expected value after subtracting the cost of the ticket.

• Cost of ticket: $5.00
• Net expected value: $0.64 - 5.00 = -4.36$

Thus, the expected value of one ticket is $-\$4.36$.

Final Answer:

A. $-\$4.36$

Would you like details or have any questions?

Here are 5 related questions:

1. How would the expected value change if more tickets were sold?
2. What is the expected value if the ticket price was reduced to $3?
3. How does the expected value compare to simply investing $5 in a savings account?
4. What is the probability of winning at least one of the prizes?
5. How would the expected value change if the value of the prizes were increased?

Tip: Understanding expected value can help in making informed decisions about participating in lotteries and raffles.