To solve this problem, we can calculate the expected number of times a four will appear when rolling a 6-sided die 2400 times.

Steps:

1. Each side of a 6-sided die has an equal probability of being rolled, so the probability of rolling a four is: $P(\text{four}) = \frac{1}{6}$

2. The expected number of times a four will appear when rolling the die 2400 times is given by: $\text{Expected number of fours} = 2400 \times P(\text{four}) = 2400 \times \frac{1}{6} = 400$

Conclusion:

The best prediction for the number of times you will roll a four is 400.

Would you like more details or have any questions? Here are five related questions you might consider:

1. How do we calculate expected values for other dice rolls?
2. What is the probability of rolling a specific number on multiple rolls of the die?
3. What is the variance in the number of times a four will appear in 2400 rolls?
4. How would the prediction change if the die were biased?
5. How can we calculate the expected number of times two different numbers will appear?

Tip: The expected value for any outcome of a dice roll can be found by multiplying the probability of that outcome by the number of rolls.