A sample space consists of ordered pairs where the first item is a lower-case Greek alphabet from the set {a.B.y, 8,e,a} and the second item is from the set of number 0-9 (An example of an element from the sample space is (a, 1)). Answer the following questions. (Assume all elements in the sample space are equally probable.) Define the following 3 events A, B and E as: The event labeled A is the set of elements with first item a. The event labeled B is the set of elements with first item B and only odd digits. The event labeled E is the set of elements with only even digits. a. How many elements are in the sample space? b. How many elements are in each event A, B and E? c. Find the probability of the event E. d. Find the probability of the event AC. e. If there are two other events labeled C and D, what is the name of the property that these two sets have, if P(C U D) = P(C) + P(D) ? Create your own sets Cand D from this sample space that satisfy this property. f. If you have two independent sets labeled G and H and wanted to compute the probability of the intersection, why is the statement P(G) n P(H) nonsensical? Write out the correct statement to find the probability of this intersection, and the way you would find it using the property of independence. 8. What property can you say the two events B and EC have? Write out the relationship between the two events mathematically. What can you say about the relationship between P(B) and P(E)(do not compute them, only state the relationship using =x, or >. h. Find the probability of the event Bn E. Are the two events B and E independent (mathematically support your answer)? i. Find the following conditional probability P(BIE).