# Two dice are rolled together and X is the highest score minus the lowest score of the dice. What are the possible values of X?

##### 1 Answer

If you consider just positive number, you have 15 possible values, if you also consider negatives, including zero, you have 31 possible values, with zero occurring with higher probability.

#### Explanation:

First of all, this question should be reformulated, if you have two dice, what is the meaning of higher and lower scores if they are just two? it seems meaningless. I am going to answer the question:

**Two dice are rolled together and X is the difference of the scores of the dice. What are the possible values of X?**

Consider two independent dice; it means that the probability of one does not affect the other, mathematically:

**Case 1: positive and negative numbers are valid **

In this case, we have:

**Case 2: * just positive numbers are valid* **

In this case, we have, since the order does matter:

**Conclusions**

To know the values, just take the maximum,

**See**