If a single six-sided number cube is rolled twice, what is the probability that the sum is greater than 5, given that the first roll was a 3?

If the first roll is 3, the sum will be greater than 5 if the second roll is 3 or greater. There are 4 numbers out of the 6 on the die that are 3 or greater.

The probability of rolling a 3 or greater is 4/6 = 2/3.