The problem in the image appears to involve a modified die with numbers 1 through 6 on each face. Here is a summary of the problem details:

1. You have a fair, six-faced die with numbers from 1 to 6.
2. The die is modified so that the probability of one particular number appearing is $\frac{1}{4}$, while the probabilities of the other numbers are different.
3. The expected value of the result (the number that comes up) is 3.
4. You need to determine the number on the opposite face of the side with 3.

To solve this problem, we need to apply probability concepts and possibly set up equations based on the information about probabilities and expected values.

Would you like a step-by-step explanation of the solution process, or do you have any specific questions about the problem setup?

Here are some questions related to this problem that could expand on this topic:

1. How do we calculate expected values for non-uniform probability distributions?
2. How would the expected value change if all faces of the die had equal probabilities?
3. What are common ways to modify probabilities in real-world dice games?
4. How can we mathematically confirm which face is opposite a given number on a standard die?
5. How can conditional probability be used in problems involving dice?

Tip: When dealing with modified probability distributions, setting up an equation for the expected value based on known probabilities can simplify complex probability problems.