A fair die is thrown once. Let A: “the number obtained is even”, B: “the number obtained is a multiple of 3”.
a. (i) Calculate P(A), P(B) and P(A∩B).
b. (ii) Verify whether the events A and B are independent, showing all steps clearly.
c. (iii) If the die is thrown a second time independently of the first throw, find the probability that event A occurs in the first throw while event B does not occur in the second throw. State clearly any property of independence you use.