1. A fair six-sided die is tossed, and the up face is noted. If the number is 2, a fair coin is tossed. Define the events: A: {A tail appears on the coin, and B: {The die is tossed only one time} a) List the sample points in the sample space [ Hint: there are 20 sample points]. b) Give the probability for each of the sample points. c ) Find P(A) and P(B). d) Identify the sample points in A, B, An B, and A U B. e) Find P(A), P(B ), P(A n B), P(A U B), P(A | B), and P(B | A). f) Are A and B mutually exclusive events? Why? g) Are the events A and B independent? Justify your answer using an equation