May I please get help with a and b

Introductory I Tooability 1. (a) Let { B1, B2,.. .} be events that are pairwise mutually exclusive and exhaustive, and A, C be arbitrary events. Show that P(AC) - P(AB, n C)P(B, C) b) Train tickets are distributed into three boxes. Each ticket can be classified as either First Class (FC) or Third Class (TC) and as either Long Distance (LD) or Short Distance (SD). Each box contains the following proportions of tickets of each type: Box FC and SD FC and LD TC and SD TC and LD Box 1 10% 25% 15% 50% Box 2 24% 22% 33% 21% Box 3 40% 40% 10% 10% A box is randomly selected and a ticket is randomly chosen from that box. Given that the chosen ticket is a first class ticket, what is the probability that it is a long distance ticket