A die is rolled twice. What is the probability of showing a 3 on the first roll and an even number on the second roll?

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Question Help: $\square$ Video

Step 1 ：The problem is asking for the probability of two independent events: rolling a 3 on the first roll and rolling an even number on the second roll.

Step 2 ：The probability of rolling a 3 on a six-sided die is \(\frac{1}{6}\) because there is only one 3 on a die and there are six possible outcomes.

Step 3 ：The probability of rolling an even number on a six-sided die is \(\frac{1}{2}\) because there are three even numbers (2, 4, and 6) and six possible outcomes.

Step 4 ：Since these are independent events, we can multiply the probabilities together to get the overall probability.

Step 5 ：\(prob\_3 = 0.16666666666666666\)

Step 6 ：\(prob\_even = 0.5\)

Step 7 ：\(overall\_prob = prob\_3 \times prob\_even = 0.08333333333333333\)

Step 8 ：Final Answer: The probability of rolling a 3 on the first roll and an even number on the second roll is \(\boxed{0.0833}\) or \(\boxed{\frac{1}{12}}\).