1. Give the answers to the following parts with proper working; (a) A three digit winning lottery number is selected. What will be the list of sample space and total number of sample point in that list of the events if the events are defined as follow: A = The last digit is 9 B = All three digits are similar (b) Each of three men fire one shot at a target. Let A: the event that the target is hit by Man-1, B: the event that the target is hit by Man-2, C: the event that the target is hit by Man-3. If also we assume that, P(A) = 0.75, P(B) = 0.90, P(C) = 0.85, then compute the probability that: (i) Exactly two men hit the target. (ii) At least one man hit the target. (iii) At most two men hit the target. (iv) None will hit the target. (c)Two teams A and B play a tournament of CHESS. The rule is decided that the team who wins two games in succession or wins three games in all, wins the tournament. List all the possible outcomes of the tournament. (d)A salesman figures that the probability of making a sale on the first call is 0.40. If he makes subsequent calls on the same person who has not yet bought, the probability falls by 0.1 on each call. What is the probability of selling the product: (i) On third call. (ii) on three calls. (iii) on the sequence of 4 calls. (E) If a permutation word is selected at random from the given word, "COURAGE", then what is the probability of the permutation word: (i) Consonant comes in even places. (ii) C and E comes together. (iii) A and E occupy on the ends