Given that he arrives on City D on the train he hoped to catch, what is the probability he does so on time?

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
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Given that he arrives on City D on the train he hoped to catch, what is the probability he does so on time?

A professor is traveling by rail from City A to City D, and he must change trains at City B and City C.
Because his connection times are very short, he fears that his arrival in City D will be nowhere close to
schedule.
Specifically, he estimates the chance of lateness as 30% for both City A-B and City B-C train con-
nections, and as 20% for City C-D connections. A late train is behind schedule throughout its trip. It is
assumed that all trains that are not late are on schedule and lateness of trains are independent of each other.
At each junction, professor will miss his connection if the arriving train is late and departing one is on
schedule. Otherwise, he will catch the train.
Transcribed Image Text:A professor is traveling by rail from City A to City D, and he must change trains at City B and City C. Because his connection times are very short, he fears that his arrival in City D will be nowhere close to schedule. Specifically, he estimates the chance of lateness as 30% for both City A-B and City B-C train con- nections, and as 20% for City C-D connections. A late train is behind schedule throughout its trip. It is assumed that all trains that are not late are on schedule and lateness of trains are independent of each other. At each junction, professor will miss his connection if the arriving train is late and departing one is on schedule. Otherwise, he will catch the train.
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