Answer all questions with explanation

(b) Puzzle: Suppose you dene a probability space (9, A, P). Please determine if the following statement is logically consistent or not and why: \"For three sets A, B , C E A, P[A] = P[B] = P[C] = 2/5, P[A n B] = PM P: C] = P[B n C] = 4/25, P[An B H C] = 4/125.\" (d) Assume Q is a sample space. Enumerate all sets belonging to an algebra which includes sets A and B that are disjoint. (e) If the answer is yes, then is A independent of B, is A independent of C, and is B independent of 0? Are A, B and 0 independent