Q.1 (a). (6') Define the sample space ? ={1, 2, 3, 4, 5, 6, 7} and the sets: A = (2, 3, 7}, B = {1, 3, 6} and C= (4). What are the elements of the sets corresponding to the following events? (i). ACUBC (ii). (ACUB)n(Acncc ) (b). (4') Given the following three-circle Venn Diagram, shade the portion corresponding to the set: Acn(B'nC) (c). (12') True or False? (i). Empty set contains no element { }. (ii). If two sets A and B are disjoint, and they form a partition of the sample space ?, then P(A) = 1 - P(B). (iii). If A is independent of B and A is independent of C, then B is independent of C. (iv). P(B|A) P(B) = P(A|B)P(A) (v). P(AUBUC) = P(A) + P(B) + P(C) - P(AnB) - P(AnC) - P(BnC) + P(AnBnc) (vi). The 2nd moment of the random variable X is the variance of X. (d). (4') A pair of fair 6-sided dice is rolled once. Find the probability that the first die is a "2" given that the faces sum to "8"