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.*2 points2/75/61/63/7

To solve this problem, we need to understand the sample space and the favorable outcomes.

Step 1: Identify the sample space When two dice are thrown, the total number of outcomes is 36 (6 outcomes from the first die multiplied by 6 outcomes from the second die).

Step 2: Identify the favorable outcomes for the event that the sum of the two dice is even The sum of two dice can be even if both are even or both are odd. The even outcomes on a die are 2, 4, 6 and the odd outcomes are 1, 3, 5. So, the favorable outcomes are (2,2), (2,4), (2,6), (4,2), (4,4), (4,6), (6,2), (6,4), (6,6) for both dice being even and (1,1), (1,3), (1,5), (3,1), (3,3), (3,5), (5,1), (5,3), (5,5) for both dice being odd. That gives us a total of 18 favorable outcomes.

Step 3: Identify the favorable outcomes for the event that one of the die is 2 If one of the die is 2, the outcomes can be (2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (1,2), (3,2), (4,2), (5,2), (6,2). That gives us a total of 11 favorable outcomes.

Step 4: Identify the favorable outcomes for both events occurring The outcomes where one die is 2 and the sum is even are (2,2), (2,4), (2,6), (4,2), (6,2). That gives us a total of 5 favorable outcomes.

Step 5: Calculate the probability The probability of both events occurring is the number of favorable outcomes divided by the total number of outcomes. So, the probability is 5/36.