Q1. Given the equally-likely sample space S = {1, 2, 3, 4, 5, 6, 7, 8,9, 10, 11, 12}, and the events E = {4, 8, 12} F = {2, 4, 6, 8, 10, 12} G = {3, 9} Determine, with justification, each of the following. (a) P(E) (b) P(G') (c) P(EUF) (d) P(EnG) (e) P(EF) (f) P(FE) Q2. The following table gives the inventory of 125 books in a corner store. Mystery Romance Thriller Totals Paperback books |50 25 20 95 Hardcover books 10 15 5 30 Totals 60 40 25 125 (a) What is the probability that a book chosen at random is a mystery? (b) What is the probability that a book chosen at random is a paperback? (c) What is the probability that a book chosen at random is a paperback, given that it is a thriller? (d) What is the probability that a book chosen at random is a romance, given that it is a hardcover? (e) What is the probability that a book chosen at random is a mystery or thriller, given that it is a paperback? (f) What is the probability that a book chosen at random is a hardcover book, given that it is a mystery or a romance? Q3. A jar contains three cubes: a red cube, a green cube, and an orange cube. A second jar contains 5 balls numbered 1 to 5. A six-sided die is also available. I An experiment is conducted where one cube is selected from the first jar, one ball is selected from the second jar, and the six-sided die is rolled. The colour of the cube, the number on the ball, and the number on the six-sided die are recorded. (a) Let event E be the event that the cube is either red or orange, the number on the ball is even, and the number on the die is even. Determine, with justification, P(E). (b) Let event F be the event that the sum of the number on the ball and the number on the die is greater than or equal to 5. Determine, with justification, P(F). events E and F. (c) Determine, with justification, P(E n F), the probability that the outcome satisfies both