To find the expected value of the raffle, we need to calculate the expected value $E(X)$ of the random variable $X$, which represents the amount won on a single raffle ticket.

The expected value is calculated as follows:

$E(X) = \sum (x_i \cdot p_i)$

where $x_i$ is the value of each prize, and $p_i$ is the probability of winning that prize.

Here are the given prizes and their probabilities:

• 1 prize of $700: $\frac{1}{5000}$
• 3 prizes of $200: $\frac{3}{5000}$
• 5 prizes of $10: $\frac{5}{5000}$
• 20 prizes of $5: $\frac{20}{5000}$
• The rest of the tickets (4971) win $0: $\frac{4971}{5000}$

Let's calculate each part:

1. For the $700 prize: $700 \times \frac{1}{5000} = 0.14$

2. For the three $200 prizes: $200 \times \frac{3}{5000} = 0.12$

3. For the five $10 prizes: $10 \times \frac{5}{5000} = 0.01$

4. For the twenty $5 prizes: $5 \times \frac{20}{5000} = 0.02$

5. For the $0 prize: $0 \times \frac{4971}{5000} = 0$

Adding these together gives the expected value:

$E(X) = 0.14 + 0.12 + 0.01 + 0.02 + 0 = 0.29$

Therefore, the expected value of the raffle if you buy 1 ticket is $\boxed{0.29}$ dollars.

Do you want details or have any questions?

Here are 5 more questions you might ask:

1. How do I calculate the variance of the raffle ticket winnings?
2. What is the probability of not winning any prize in this raffle?
3. How would the expected value change if the number of tickets sold was different?
4. How can I use expected value in other types of lotteries or games of chance?
5. What does the expected value tell me about the fairness of the raffle?

Tip: When calculating expected values, ensure all possible outcomes and their probabilities are accounted for to achieve accurate results.