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 U B, and A ^c
2. Find P(A), P(B), P(A \(\cap \) B), P(A U B), and P(A ^C ) by summing the probabilities of the appropriate sample points.
3. Find P(A U 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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