please show proper working.

Find the probabilities of the following: (1.1. Suppose we have a sample space with five equally likely outcomes: 01. Oz. 03, (1,, 05. Lat A = {01: 03} B = {02! 01} C = {02! 03: 05} (a) Find Fm). ['03]. HQ. (b) Find PM U B], P[B U C). [c] Find Pm)\". P03)\". PUG)". [d] Find Philc U 3'), Pull U B)\". [e] Are A, B and C are Mutually Exclusive. Non Mutually Exclusive, Collectively Exhaustive? {1.2. A pair of fair dice is rolled once. What is the probability that: (a) First dot is 4 or 6 and second dot is 3 or 5. (b) Both dots are prime numbers. [c] Neither be the multiple of 5. [d] First is less than Second or second is less than rst (e) First is at least 4 and second is at most 3 {1.3. Three fair coins are tossed together. What is the probability of getting: (a) All Heads (b) At least 2 Heads [c] At most 2 Heads [d] None Head [e] Head must he appeared {1.4. From a deck of 52 cards. four cards are drawn at random. What is the probability that: (a) All cards are from same suits. (b) All are of Ace. [c] All are of Face cards. [d] All are of Picture cards. (e) All are of the same colors