Question: A pair of fair dice is tossed. Define the following events:

\(A:\{\) You will roll a 7 \(\}\) (i.e., the sum of the dots on the up faces of the two dice is equal to 7 )

\(B:\{\) At least one of the two dice shows a 4 \(\}\)

1. Identify the sample points in the events \(A, B, A \cap B\), \(A \cup B\), and \(A^{c} .\)
2. Find \(P(A), P(B), P(A \cap B), P(A \cup B)\), and \(P\left(A^{c}\right)\) by summing the probabilities of the appropriate sample points.
3. Find \(P(A \cup B)\) using the additive rule. Compare your answer to that for the same event in part b.
4. Are \(A\) and \(B\) mutually exclusive? Why?

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