A fair 6-sided die is rolled three times. What is the probability of rolling an even number at least once?

To find the probability of rolling an even number at least once when a fair 6-sided die is rolled three times, we can use the complement rule. The complement rule states that the probability of an event happening is 1 minus the probability of the event not happening.

Step-by-step solution:

1. Identify the total number of outcomes for one roll: A fair 6-sided die has 6 faces, so there are 6 possible outcomes for each roll.

2. Determine the probability of rolling an even number in one roll: The even numbers on a 6-sided die are 2, 4, and 6. There are 3 even numbers out of 6 possible outcomes. Probability of rolling an even number in one roll = 3/6 = 1/2.

3. Determine the probability of not rolling an even number in one roll: If the probability of rolling an even number is 1/2, then the probability of not rolling an even number is also 1/2.

4. Calculate the probability of not rolling an even number in three rolls: Since each roll is independent, we multiply the probabilities for each roll. Probability of not rolling an even number in three rolls = (1/2) * (1/2) * (1/2) = (1/2)^3 = 1/8.

5. Calculate the probability of rolling an even number at least once: Using the complement rule, we subtract the probability of not rolling an even number in three rolls from 1. Probability of rolling an even number at least once = 1 - Probability of not rolling an even number in three rolls. Probability of rolling an even number at least once = 1 - 1/8 = 7/8.

Therefore, the probability of rolling an even number at least once when a fair 6-sided die is rolled three times is 7/8.