(a) Under what circumstances is an event A independent of itself? 

(b) By considering events concerned with independent tosses of a r ~ d die and a blue die, or otherwise. give examples of events A, B and C which are not independent, but nevertheless are such that every pair of them is independent. 

(c) By considering events concerned with three independent tosses of a coin and supposing that A and B both represent tossing a head on the first trial, give examples of events A. /3 and C which are such that P(ABC) = P(A)P(B)P(C) although no pair of them is independent.