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# ismch04 - Chapter 4 Probability 45 Chapter 4 Probability...

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Chapter 4: Probability 45 Chapter 4: Probability 4.1. a. The complement of event A is that it will take 4 days or less before the machinery becomes operational. b. The intersection of A and B will be the event that it takes 5 days before the machinery becomes operational. c. The union of A and B is the event of 1 day, 2 days, 3 days, 4 days, 5 days, 6 days or 7 days d. A and B are not mutually exclusive because P(A B) 0 e. Yes A and B are collectively exhaustive because they include all of the possible sample points f. (A B) is the event that it takes 5 days. ( A B) is the event that it takes 4 days, 3 days, 2 days, 1 day. The union between these two events is that it takes less than 6 days (1 through 5) before the machinery is operational. This is the definition of event B, therefore (A B) ( A B) = event B g. ( A B) is the event that it takes 4 days, 3 days, 2 days, 1 day. Since A is the event 5 days, 6 days, 7 days, Then A ( A B) will be the event of 1 through 7 days. This is the event of A B. Therefore, A ( A B) must equal A B. 4.2. a. (A B) is the event that the Dow-Jones average rises on both days which is O 1 . ( A B) is the event the Dow-Jones average does not rise on the first day but it rises on the second day which is O 3 . The union between these two will be the events O 1 O 3 which by definition is event B: the Dow-Jones average rises on the second day. b. Since ( A B) is the event the Dow-Jones average does not rise on the first day but rises on the second day which is O 3 and because A is the event that the Dow- Jones average rises on the first day, then the union will be the event that either the Dow-Jones average does not rise on the first day but rises on the second day or the Dow-Jones average rises on the first day or both. This is the definition of A B. 4-3. a. Sample points in the sample space include the following 20 simple events: M1,M2 M2,M1 M3,M1 T1,M1 T2,M1 M1,M3 M2,M3 M3,M2 T1,M2 T2,M2 M1,T1 M2,T1 M3,T1 T1,M3 T2,M3 M1,T2 M2,T2 M3,T2 T1,T2 T2,T1 b. Event A is that at least one of the two cars selected is a Toyota c. Event B is that the two cars selected are the same model d. The complement of A is the event that the customers do not select at least one Toyota e. (A B) is the event that at least one Toyota is selected and two cars of the same model are selected. Since ( A B) is the event that the customers do not select at least one Toyota and two cars of the same model are selected, then

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46 Instructor’s Solutions Manual for Statistics for Business & Economics, 5 th Edition the union between the two events will be the event that two cars of the same model are selected. This is the definition of event B. f. ( A B) is the event that the customers do not select at least one Toyota and two cars of the same model are selected. Since A is the event that the customers select at least one Toyota, then the union between the two will be the event that at least one Toyota is selected or the two cars of the same model are selected or both. This is the definition of event A B 4-4.
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