Final answer:
The probability of rolling a 5 given that an even number has been rolled on a fair six-sided die is zero because 5 is not an even number.
Step-by-step explanation:
The student has asked about the probability of a specific outcome when rolling a fair six-sided die.
Given that they have rolled an even number, the probability that the die shows a 5 is being questioned.
Since 5 is not an even number, the probability of rolling a 5 given that the outcome is even is zero.
To perform this calculation, we consider the conditional probability.
The even numbers on a die are {2, 4, 6}. Since 5 is not in this set, there are no favorable outcomes over the total possible even outcomes, which makes the probability 0.