Conditional Dice Roll

We are told that a fair 6-sided die is rolled, and we want to find the probability that the number is greater than 4 given that it is even. This is a conditional probability problem, where we are conditioning on the number being even. First, let's identify the sample space of even outcomes on a 6-sided die. The even numbers are \( \{2, 4, 6\} \), so there are 3 equally likely outcomes under the condition that the roll is even. Now, out of those even numbers, how many are greater than 4? Only one of them — the number 6 — satisfies this condition. Therefore, the conditional probability is: \[ P(\text{greater than 4} \mid \text{even}) = \frac{\text{Number of favorable even outcomes}}{\text{Number of even outcomes}} = \frac{1}{3} \] So, the probability that the die shows a number greater than 4, given that it is even, is \( \frac{1}{3} \).