3. (6 points) Let (0, F, P) be a finite discrete probability space. Fix A E F such that P(A) > 0. Let ?' = A and let F' = {S : SC n'}. That is, ' and F' are the restrictions of ? and F to A. Show that P(.| A) is a probability function associated with ?', F'. (a) (2 points) (First axiom) Show that P(B| A) E [0, 1] for all BE F'. (b) (3 points) (Second axiom) Let B, C E F', where BNC = 0. Show that P(B U CA) = P(B|A) + P(CA). (c) (1 point) (Third axiom) Show that P(S'|A) = 1