Two dice are rolled at the same time. The first die shows a 2. Given that is a random variable that represents the sum of the results shown by the two dice, what are the possible values of X?

3 ≤ X ≤ 8

Step-by-step explanation:

A die has 6 faces numbered from 1 to 6.

If two dice are rolled at the same time and the first die already shows a 2. Then the second die will show any number between 1 and 6 inclusive.

X which is the sum of the results shown by the dice will always be greater than or equal to 3 but less than or equal to 8. This is because the first die already shows a 2 and the second die will always be a number between 1 and 6 inclusive. i.e

X = result from die 1 + result from die 2

X = 2 + [1, 6]

X = [3, 8]

In other words, the minimum value of X is 3 and the maximum value of X is 8.