2) One morning, Angel sees dice and rolls it. A) If Angel rolls two dice, what is the probability that the sum of the numbers is even when rolled?

To solve this problem, we need to understand the possible outcomes when two dice are rolled.

Step 1: Identify the total number of outcomes When a die is rolled, it can land on any one of 6 faces. So, when two dice are rolled, the total number of outcomes is 6*6 = 36.

Step 2: Identify the favorable outcomes We need to find the outcomes where the sum of the numbers on the two dice is even. The possible sums are 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12. Out of these, 2, 4, 6, 8, 10, and 12 are even. The number of ways to get these sums are as follows:

• 2: 1 way (1 on both dice)
• 4: 3 ways (1 and 3, 2 and 2, 3 and 1)
• 6: 5 ways (1 and 5, 2 and 4, 3 and 3, 4 and 2, 5 and 1)
• 8: 5 ways (2 and 6, 3 and 5, 4 and 4, 5 and 3, 6 and 2)
• 10: 3 ways (4 and 6, 5 and 5, 6 and 4)
• 12: 1 way (6 on both dice) So, the total number of favorable outcomes is 1+3+5+5+3+1 = 18.

Step 3: Calculate the probability The probability of an event is the number of favorable outcomes divided by the total number of outcomes. So, the probability that the sum of the numbers is even when two dice are rolled is 18/36 = 0.5 or 50%.