Question: prove that if a and b are mutually exclusive they cannot be independent?
Answer: They are mutually exclusive if and only if P(X∩Y)=0. ... If the events are independent, then P(X)P(Y)=P(X∩Y)>0, which would imply that they are not mutually exclusive! In other words, the events cannot be both independent and mutually exclusive if both of their probabilities are greater than 0.