A fair die is tossed, and the up face is noted. If the number is less than

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A fair die is tossed, and the up face is noted. If the number is less than 3, the die is tossed again; otherwise, a fair coin is tossed. Consider the following events:

A: 5A tail appears on the coin6 B: 5The die is tossed only one time6

a. List the sample points in the sample space.

b. Give the probability for each of the sample points.

c. Find P(A) and P(B).

d. Identify the sample points in Ac, Bc, A ¨ B, and A ∪ B.

e. Find P1Ac2, P1Bc2, P1A¨ B2, P1A∪B2, P1A0B2, and P1B0A2.

f. Are A and B mutually exclusive events? Independent events? Why?

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