1 Let = {a, b, c} be a sample space. Let m(a) = 1/2, m(b) = 1/3, and m(c) = 1/6. Find the probabilities for all eight subsets of N. 2 Give a possible sample space for each of the following experiments: (a) An election decides between two candidates A and B. (b) A two-sided coin is tossed. (c) A student is asked for the month of the year and the day of the week on which her birthday falls. (d) A student is chosen at random from a class of ten students. (e) You receive a grade in this course. 3 For which of the cases in Exercise 2 would it be reasonable to assign the uniform distribution function? 4 Describe in words the events specified by the following subsets of N = {HHH, HHT, hth, htt, thH, THT, TTH, TTT} (see Example 1.6). (a) E = {HHH,HHT,HTH,HTT}. (b) E = {HHH, TTT}. {HHH,TTT}. (c) E {HHT,HTH,THH}. = (d) E = {HHT,HTH,HTT,THH,THT,TTH,TTT}. 5 What are the probabilities of the events described in Exercise 4? 6 A die is loaded in such a way that the probability of each face turning up is proportional to the number of dots on that face. (For example, a six is three times as probable as a two.) What is the probability of getting an even number in one throw? 7 Let A and B be events such that P(A B) = 1/4, P() = 1/3, and P(B) = 1/2. What is P(AUB)?