Once per minute, a subway train arrives at the XYZ station with probability p. Every time the train arrived, it is either Green, Red or Blue. Consecutive minutes are inde- pendent: for example, knowing that a train arrived or did not arrive at 10:12AM tells you nothing about what will happen at 10:13AM. Trains arriving after 10:00AM always arrive in the following order:

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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Question

Once per minute, a subway train arrives at the XYZ station with probability p. Every time the train arrived, it is either Green, Red or Blue. Consecutive minutes are inde- pendent: for example, knowing that a train arrived or did not arrive at 10:12AM tells you nothing about what will happen at 10:13AM. Trains arriving after 10:00AM always arrive in the following order: Green train always comes first, followed by the Red train, followed by the Blue train. Your train is the Blue Train.
You come to the XYZ station at exactly 10:00AM. What is the probability that you will wait exactly 10 minutes for your train?

Note:

the first time a train may or may not arrive is 10:01AM.
you should assume that the value of the probability p is known. You final answer should include p.

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