(i) Define independent events in the context of probability.
(ii) Two events A and B are such that A∩B=∅ and P(A)=0.4, P(B)=0.3. Are A and B independent? Give a detailed justification based on the definition you have stated in part (i).
(iii) Comment on whether two events that are mutually exclusive can ever be independent if both have non-zero probability. Support your answer with logical reasoning.
b. (ii) Two events A and B are such that A∩B=∅ and P(A)=0.4, P(B)=0.3. Are A and B independent? Give a detailed justification based on the definition you have stated in part (i).