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STAT 111

Question1. Suppose two dice are tossed and the numbers on the upper faces are observed. Let S denote the set of all possible pairs that can be observed. Define the following subsets of S.A: the number on the second die is even.B: the sum of the two numbers is even.C: at least one number in the pa

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STAT 111

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    1. STAT 111 Chapter Zero

    2. Question1 Suppose two dice are tossed and the numbers on the upper faces are observed. Let S denote the set of all possible pairs that can be observed. Define the following subsets of S. A: the number on the second die is even. B: the sum of the two numbers is even. C: at least one number in the pair is odd. List the elements in A,CC,AnB ,AnBC,AC?B, and ACnC.

    3. Answer1 S = { (1,1),(1,2),(1,3),(1,4),(1,5), (1,6),(2,1),(2,2)….(6,6). N(S) = 6X6 = 36. A = {(1,2),(2,2),(3,2),(4,2),(5,2),(6,2), (1,4),(2,4),(3,4),(4,4),(5,4),(6,4),(1,6),(2,6), (3,6),(4,6),(5,6),(6,6). B = {(2,2),(4,2),(6,2),(2,4),(4,4),(6,4),(2,6),(4,6),(6,6). C = {(1,1),(1,2),(1,3),(1,4),(1,5),(2,1),(2,3),(2,5),(3,1), (3,2),(3,3),(3,4),(3,5),(3,6),(4,1),(4,2),(4,5),(5,1), (5,2),(5,3),(5,4),(5,5),(5,6),(6,1),(6,3),(6,5).

    4. CC =S – C ={(2,2),(2,4),(2,6),(4,2),(4,4),(4,6), (6,2),(6,4),(6,6)} AnB = B An BC = A – B ={(1,2),(3,2),(5,2),(1,4),(3,4),(5,4),(1,6), (3,6),(5,6)} AC = {(1,3),(2,3),(3,3),(4,3),(5,3),(6,3),(1,5),(2,5),(3,5), (4,5),(5,5),(6,5),(1,1),(1,2),(1,3),(1,4),(1,5),(1,6)} AC ?B ={(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(4,2),(2,2),(6,2), (1,3),(2,3),(3,3),(4,3),(5,3),(6,3),(2,4),(4,4),(6,4),(1,5), (2,5),(3,5),(4,5),(5,5),(6,5),(2,6),(4,6),(6,6)} AC nC= AC

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