Let A, B, and C denote events. (a) Show that A is independent of itself if and only if P(A) = 0 or 1. (b) Suppose P(A) > P(B) > 0 and P (A | B) = P (B | A). Show that A and B are mutually exclusive. ...

66410 assignment
Assignment Question
Let A, B, and C denote events.
(a) Show that A is independent of itself if and only if P(A) = 0 or 1.
(b) Suppose P(A) > P(B) > 0 and P (A | B) = P (B | A). Show that A and B are mutually exclusive.
(c) Suppose that A, A ∩ B, and A ∪ Beach is independent of C. Show that B is also independent of C.
a) Let A be an event independent of itself.
We know A∩A =A by set theory
Also for independent events P(A∩B)...