As an impatient driver, I often switch lanes in a traffic jam. A certain highway has two lanes in my direction. Whenever traffic moves, if I'm in the left lane I switch to the right with a probability 50%. If I'm in the right lane I switch back to the left with a probability 80%, because it's supposed to be faster. Over the long term, what fraction of time do I expect to spend in the left lane?

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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As an impatient driver, I often switch lanes in a traffic jam. A
certain highway has two lanes in my direction.
Whenever traffic moves, if I'm in the left lane I switch to the right
with a probability 50%.
If I'm in the right lane I switch back to the left with a probability
80%, because it's supposed to be faster.
Over the long term, what fraction of time do I expect to spend in
the left lane?
(Express your answer to 3 decimal places.)
Transcribed Image Text:As an impatient driver, I often switch lanes in a traffic jam. A certain highway has two lanes in my direction. Whenever traffic moves, if I'm in the left lane I switch to the right with a probability 50%. If I'm in the right lane I switch back to the left with a probability 80%, because it's supposed to be faster. Over the long term, what fraction of time do I expect to spend in the left lane? (Express your answer to 3 decimal places.)
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