Let two dice be thrown together. Find the probability that one of the die is 2 if the sum of the two dice is even.

Step 1: Identify the total number of outcomes when two dice are thrown together. Since a die has 6 faces, the total number of outcomes is 6*6 = 36.

Step 2: Identify the outcomes where the sum of the two dice is even. The pairs (1,1), (1,3), (1,5), (2,2), (2,4), (2,6), (3,1), (3,3), (3,5), (4,2), (4,4), (4,6), (5,1), (5,3), (5,5), (6,2), (6,4), (6,6) satisfy this condition. So, there are 18 such outcomes.

Step 3: Identify the outcomes where one of the die is 2 and the sum is even. The pairs (2,2), (2,4), (2,6), (4,2), (6,2) satisfy this condition. So, there are 5 such outcomes.

Step 4: The probability of an event is given by the number of favorable outcomes divided by the total number of outcomes. Here, the total number of outcomes is the number of outcomes where the sum is even, which is 18. The number of favorable outcomes is the number of outcomes where one die is 2 and the sum is even, which is 5.

Step 5: So, the probability that one of the die is 2 given that the sum of the two dice is even is 5/18.