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Kym, Chris and Lee want to trave routes pass along their road and, wl that comes along. At any given tim probability that bus B comes first is- Al throo bucoc tormina at the can

Kym, Chris and Lee want to trave routes pass along their road and, wl that comes along. At any given tim probability that bus B comes first is- Al throo bucoc tormina at the can

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Kym, Chris and Lee want to travel together into the bus station in town. Three bus routes pass along their road and, whatever the time of day, they will catch the first bus that comes along. At any given time, the probability that bus A comes first is 0.6, the probability that bus B comes first is 0.2 and the probability that bus C comes first is 0.2. All three buses terminate at the same bus station halfway into town. If Kym, Chris and Lee catch bus A they will always catch bus D for the remaining journey to town. If they catch bus B, the probability that bus D will be first is 0.4 and the probability that bus E will be first is 0.6. If they catch bus C, the probability that bus D comes first is 0.3, the probability that bus E comes first is 0.2 and the probability that bus F comes first is 0.5. (i) Display the above information in a tree diagram. (ii) Of the possible routes that the three can travel, which is the least probable? (iii) Given that three of them catch bus D, what is the probability that they caught bus C for the first stage of the journey? (iv) What is the probability that on their journey into town the three will catch bus B or bus D but not both?
Transcribed Image Text:Kym, Chris and Lee want to travel together into the bus station in town. Three bus routes pass along their road and, whatever the time of day, they will catch the first bus that comes along. At any given time, the probability that bus A comes first is 0.6, the probability that bus B comes first is 0.2 and the probability that bus C comes first is 0.2. All three buses terminate at the same bus station halfway into town. If Kym, Chris and Lee catch bus A they will always catch bus D for the remaining journey to town. If they catch bus B, the probability that bus D will be first is 0.4 and the probability that bus E will be first is 0.6. If they catch bus C, the probability that bus D comes first is 0.3, the probability that bus E comes first is 0.2 and the probability that bus F comes first is 0.5. (i) Display the above information in a tree diagram. (ii) Of the possible routes that the three can travel, which is the least probable? (iii) Given that three of them catch bus D, what is the probability that they caught bus C for the first stage of the journey? (iv) What is the probability that on their journey into town the three will catch bus B or bus D but not both?
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