A fair die is tossed, and the up face is noted. If the number is even, the die is tossed again; if the number is odd, a fair coin is tossed. Consider the following events:
A: {A head appears on the coin.}
B: {The die is tossed only one time.}
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 P(Ac),P(Bc),P(A ∩ B), P(A ∪ B),P(A|B), and P(B|A).
f. Are A and B mutually exclusive events? Independent events? Why?
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