The day begins with the first appointment on time, or 1, 0 (S0). What are the state probabilities for periods 1, 2, and 3?

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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Appointments in a medical office are scheduled every 15 minutes. Throughout the day, appointments will be running on time or late, depending on the previous appointment only, according to the following matrix of transition probabilities:

 

Previous

Appointment

Next Appointment

On Time

Late

On Time

.70

.30

Late

.45

.55

 

The day begins with the first appointment on time, or 1, 0 (S0). What are the state probabilities for periods 1, 2, and 3?

 

Period 1 __________

 

Period 2 __________

 

Period 3 __________ 

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