ASSIGNMENT 2

ASSIGNMENT 2 - Assignment.2 solution February, 3, 2010 MATH...

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Assignment.2 solution February, 3, 2010 MATH 203 3.42 Solution : The experiment consists of rolling a pair of fair dice. The simple events are: 1 , 1 2 , 1 3 , 1 4 , 1 5 , 1 6 , 1 1 , 2 2 , 2 3 , 2 4 , 2 5 , 2 6 , 2 1 , 3 2 , 3 3 , 3 4 , 3 5 , 3 6 , 3 1 , 4 2 , 4 3 , 4 4 , 4 5 , 4 6 , 4 1 , 5 2 , 5 3 , 5 4 , 5 5 , 5 6 , 5 1 , 6 2 , 6 3 , 6 4 , 6 5 , 6 6 , 6 It can be assumed that all events are equally likely, although this does not follow from the fact that coin is fair. (a) A: { (1,6),(2,5),(3,4),(4,3),(5,2),(6,1) } B: { (1,4),(2,4),(3,4),(4,4),(5,4),(6,4),(4,1),(4,2),(4,3),(4,5),(4,6) } A B : { (3 , 4) , (4 , 3) } A B : { (1 , 4) , (2 , 4) , (3 , 4) , (4 , 4) , (5 , 4) , (6 , 4) , (4 , 1) , (4 , 2) , (4 , 3) , (4 , 5) , (4 , 6) , (1 , 6) , (2 , 5) , (5 , 2) , (6 , 1) } A c : { (1 , 1) , (1 , 2) , (1 , 3) , (1 , 4) , (1 , 5) , (2 , 1) , (2 , 2) , (2 , 3) , (2 , 4) , (2 , 6) , (3 , 1) , (3 , 2) , (3 , 3) , (3 , 5) , (3 , 6) , (4 , 1) , (4 , 2) , (4 , 4) , (4 , 5) , (4 , 6) , (5 , 1) , (5 , 3) , (5 , 4) , (5 , 5) , (5 , 6) , (6 , 2) , (6 , 3) , (6 , 4) , (6 , 5) , (6 , 6) } (b) P ( A ) = 6 ( 1 36 ) = 6 36 = 1 6 Using Axiom 3, since A is the disjoint union of its sample points (elementary out comes). i.e. we can just add the
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ASSIGNMENT 2 - Assignment.2 solution February, 3, 2010 MATH...

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