The elevator of a building with a ground floor and two floors makes trips from one floor to another. The floor at which the nth elevator trip ends follows a Markov chain. It is known that half of the trips that leave from the ground floor go to each of the other two floors, while if a trip starts on the first floor, only 25% of the time it ends on the second. Finally, if a journey begins on the second floor, it always ends on the ground floor. How many trips on average will a person who is on the ground floor and wants to get to the second floor make?

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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The elevator of a building with a ground floor and two floors makes trips from one floor to another. The floor at which the nth elevator trip ends follows a Markov chain. It is known that half of the trips that leave from the ground floor go to each of the other two floors, while if a trip starts on the first floor, only 25% of the time it ends on the second. Finally, if a journey begins on the second floor, it always ends on the ground floor.

How many trips on average will a person who is on the ground floor and wants to get to the second floor make?

 

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