A die is rolled twice. What is the probability of showing a 1 on the first roll and an even number on the second roll?
Your answer is :

Step 1 ：We are given a die is rolled twice. We need to find the probability of showing a 1 on the first roll and an even number on the second roll.

Step 2 ：The probability of a single event occurring is calculated by dividing the number of favorable outcomes by the total number of outcomes. In this case, we are looking for the probability of two independent events occurring, which is calculated by multiplying the probabilities of each event.

Step 3 ：For the first roll, the favorable outcome is rolling a 1, and there is only one way to do this out of six possible outcomes (the numbers 1 through 6 on the die). So the probability of rolling a 1 is \(\frac{1}{6}\).

Step 4 ：For the second roll, the favorable outcomes are rolling an even number. There are three ways to do this (rolling a 2, 4, or 6) out of six possible outcomes. So the probability of rolling an even number is \(\frac{3}{6}\), or \(\frac{1}{2}\).

Step 5 ：Since these are independent events, we multiply the probabilities together to get the overall probability. So, the overall probability is \(\frac{1}{6} \times \frac{1}{2} = \frac{1}{12}\).

Step 6 ：Final Answer: The probability of rolling a 1 on the first roll and an even number on the second roll is \(\boxed{\frac{1}{12}}\).