Answer the following questions related to the basic concepts of probability.
a. (i) Define independent events.
b. (ii) Define mutually exclusive events.
c. (iii) With mathematical reasoning, explain whether two events A and B with P(A)>0 and P(B)>0 can be both independent and mutually exclusive.
d. (iv) Give one real-life example of a pair of events that are independent but not mutually exclusive, and justify your choice.