Suppose that four letters are selected from the collection of 15 letters {A,B,..., O } at random, with replacement, and written in order to form a random "word" . Note that this is a string of 4 letters and need not be a word in any language. (a) [3 points] Let S denote the sample space consisting of all outcomes of this experiment. Give the set 8 including the first few elements. Compute the number of outcomes in S. (b) [3 points] Let A be the event that the word begins and ends with a consonant. Compute P(A). (c) [3 points] Let B be the event that the word contains all distinct letters. Compute P(B). (d) [4 points] Compute P(A n B). Are A and B independent events? Justify your answer: (d) [4 points] A small lottery is conducted as follows: You hold a ticket with the letters "FADE" . When the word is selected above, we count how many of your letters are in the selected word. (for example if the word were "MADE this number would be 3). Your prize depends on this number. Let C: More than 3 of your letters are in the random word. Find P(C)