A fair six-sided die is thrown once. Let the sample space be denoted by S and consider the event A : “the number obtained is even.” Answer the following questions:
a. (i) List explicitly all the elements of S.
b. (ii) Write the set A and its complement A′.
c. (iii) By counting outcomes, show that P(A′)=1−P(A).
d. (iv) State, with reasons, whether A and A′ are mutually exclusive events and whether they are exhaustive events.