Let's recheck the calculations to ensure the expected value is correct. 

Given the 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: $\frac{4971}{5000}$

We calculate the expected value $ E(X) $ using the formula $ E(X) = \sum (x_i \cdot p_i) $.

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:
\[ 5 \times \frac{20}{5000} = 0.02 \]

Now let's add these values together:

\[ 0.14 + 0.12 + 0.01 + 0.02 = 0.29 \]

So the expected value $ E(X) $ remains $ 0.29 $ dollars. 

The correct expected value of the raffle if you buy 1 ticket is indeed $ \boxed{0.29} $ dollars.

Please let me know if you have any other questions or if there's any part of the calculation you would like to go over again.

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: Double-checking calculations helps ensure accuracy, especially when dealing with probabilities and expected values.

Understand how to calculate the expected value of raffle prizes, including $700, $200, $10, and $5 prizes with probabilities. Learn the step-by-step method to determine the correct expected value of the raffle, ensuring accuracy in probability calculations. Suitable for advanced high school students and learners interested in probability and raffle mathematics.

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