1) An experiment results in one of the following sample points: E1, E2, Es, or E4, Find P(E4) for each of the following cases. [15 Points]~ a. P(E1) = .1, P(E2) = .2, and P(E3) = .3- b. P(E1) = P(E2) = P(E;) = P(E4)~ c. P(E1) = P(E2) = .1 and P(E3) = P(E4)~ 2) Compute the number of ways you can select n elements from N elements for each of the following: [15 Points]~ a. n = 2, N = 54 b. n = 3, N=64 c. n = 5, N = 20-3) A number between 1 and 10, inclusive, is randomly chosen, and the events A and B are defined as follows: [20 Points]~ A: { The number is even. } ~ B: { The number is less than 7. } ~ a. Identify the sample points in the event A U B.~ b. Identify the sample points in the event A n B.~ c. Which expression represents the event that the number is even or less than 7 or both?- d. Which expression represents the event that the number is both even and less than 7?~4) A pair of fair dice is tossed. Define the following events: [30 Points]~ A: { Exactly one of the dice shows a 1. } ~ B: { The sum of the numbers on the two dice is even. }~ a. Identify the sample points in the events A, B, A n B, and A U B. [10 Points] b. Find P(A), P(B), P(4 ( B), and P(A U B) by summing the probabilities of the appropriate sample points. [10 Points]~ c. Using your result from part b, explain why A and B are not mutually exclusive. [5 Points]~ d. Find P(A U B) using the additive rule. Is your answer the same as in part b? [5 Points]