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 analyze the events defined by the question and determine which pairs of these events are mutually exclusive.

### Step 1: Define the Sample Space
When rolling a pair of dice, the sample space consists of all possible outcomes. Each die has 6 faces, so the total number of outcomes when rolling two dice 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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