An experiment involves rolling a pair of dice and recording the numbers that come up. Describe the following events:A: the sum is greater than 8, B: 2 occurs on either dieC: the sum is at least 7 and a multiple of 3.Which pairs of these events are mutually exclusive?

Explanation

To solve the problem, we need to define the events A, B, and C based on the outcomes of rolling two dice, and then determine which pairs of these events are mutually exclusive.

### Step 1: Define the Sample Space
When rolling two dice, the sample space \( S \) consists of all possible outcomes. Each die has 6 faces, so the total number of outcomes is \( 6 \times 6 = 36 \). The sample space can be represented as:
\[ S = \{(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (3,1), (3,2), (3,3), (3,4), (3,5), (3,6), (4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (5,1), (5,2), (5,3), (5,4), (5,5), (5,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6)\} \]

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