Please show me your work. And be clear when you explain it to me.

11) Consider the sample space for rolling two dice below: 15 points Die 2 Die 1 2 3 4 5 6 (1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6) (2, 1) (2, 2) (2, 3) (2, 4) ) (2, 5) (2, 6) (3, 1) LAWN (3, 2) (3, 3) (3, 4) (3, 5) (3, 6) (4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6) (5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6) (6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6) a) Complete the probability distribution for sum of two dice. X 2 3 4 5 6 7 8 9 10 11 12 P(X) b) Expected value of the distribution. 12) When two dice are rolled, find the probability of getting the following: 6 points a) A sum of 5 or 6 . b) A sum greater than 9. c) A sum less than 4 or greater than 9. d) A sum that is divisible by 4. e) A sum of 14. f) A sum less than 13