Question

Suppose that two balanced dice are rolled. Let X denote the absolute value of the difference of the two numbers. What are the possible values of the random variable X?

a. 0
b. 1
c. 2
d. 3

Answer 1

The possible values of the random variable X, representing the absolute value of the difference between two rolled dice, are 0, 1, 2, and 3.

Step-by-step explanation:

The random variable X represents the absolute value of the difference between the two numbers rolled on two balanced dice.

Since the dice are balanced, they have an equal probability of landing on any number from 1 to 6. When determining the possible values of X, we consider all the possible differences between the two numbers rolled.

1. If both dice land on the same number, the difference is 0. So, X can take the value 0.
2. If one die shows a higher number than the other, the difference is 1. For example, if one die shows a 6 and the other shows a 5, the difference is 1. So, X can take the value 1.
3. If there is a difference of 2, it means that one die shows a number that is 2 higher than the other. For example, if one die shows a 6 and the other shows a 4, the difference is 2. So, X can take the value 2.
4. Similarly, if there is a difference of 3, it means that one die shows a number that is 3 higher than the other. For example, if one die shows a 6 and the other shows a 3, the difference is 3. So, X can take the value 3.

Therefore, the possible values of the random variable X are 0, 1, 2, and 3. The correct option is d. 3.