Homework+2+Solutions

Homework+2+Solutions - Homework 2 Introduction to...

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Homework 2 Introduction to Probability Solutions (80 points) 1. (10 points, 5 points each) a. A reasonable sample space consists of the number of papers that are sold by the newspaper boy, S1 = {0, 1, 2, …, 9, 10}. Another one can be the number of papers that are demanded, S2 = {0, 1, 2, …, 10,11, …}. For S1, the event sets are as follows: A = {5, 6, 7, …, 10}, B = {0, 1, 2, 3, 4, 5}, C = {5}. For S2, the event sets are: A = {5, 6, 7, …}, B = {0, 1, 2, 3, 4, 5}, C = {5}. b. A reasonable sample space consists of pairs which includes the number of papers that are sold in each day, S = S1 × S1 = {(0,0), (0,1), (0,2),…,(0,10), (1,0), (1,1), (1,2),…,(1,10), …, (10,0),(10,1),(10,2),…,(10,10)}. For sample space S, event sets are as follows: A = {(5,0), (5,1), …, (5,10), (6,0), (6,1), (6,2), …,(6,10), …,(10,0), (10,1), (10, 2), …, (10,10)} B = {(0,5), (0,6), …, (0,10), (1,5), (1,6), …, (1,10), …, (10,5), (10,6), …,(10,10)} C = {(5,5), (5,6), …,(5,10), (6,5), (6,6), …, (6,10), …, (10,5), (10,6), …,(10,10)} 2. (16 points, 4 points each) The probabilities of different events are given in figure above. Using the diagram, we have a) P(A) = 0.8 b) P(B) = 0.5 c) ) ( B A P = 0.9 d) ) ( B A P = 0.6 A B 0.4 0.1 0.1 0.4
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3. (12 points, 6 points each) a) Let B1 and M1 denote selecting a blue ball and a maze ball in first stage respectively. Similarly, Let B2 denote selecting a blue ball
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Homework+2+Solutions - Homework 2 Introduction to...

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