A die is rolled twice. What is the probability of showing a 5 on the first roll and an even number on the second roll? Your answer is:

Let the sample space be all ordered pairs \((X, Y)\) where \(X\) is the outcome of the first roll and \(Y\) is the outcome of the second roll. There are \(6 \times 6 = 36\) possible outcomes. **Step 1: Find the probability of rolling a 5 on the first roll.** The probability is: \[ P(X=5) = \frac{1}{6} \] **Step 2: Find the probability of rolling an even number on the second roll.** The even numbers on a die are \(2, 4,\) and \(6\), so the probability is: \[ P(Y \text{ is even}) = \frac{3}{6} = \frac{1}{2} \] **Step 3: Calculate the combined probability.** Since the two rolls are independent events, we multiply the probabilities: \[ P(\text{5 on first roll and even on second roll}) = \frac{1}{6} \times \frac{1}{2} = \frac{1}{12} \] Final Answer: \[ \boxed{\frac{1}{12}} \]