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The Taxi Problem A taxi company has divided the city into three regions - Northside, Downtown, and Southside. By keeping track of pickups and deliveries, the company has found that of the fares picked up in Northside, 50% stay in that region, 20% are taken Downtown, and 30% go to Southside. Of the fares picked up Downtown, only 10% go to Northside, 40% stay Downtown, and 50% go to Southside. Of the fares picked up in Southside, 30% go to each of Northside and Downtown, while 40% stay in Southside. We would like to know what the distribution of taxis will be over time as they pick up and drop off successive fares. Suppose we want to know the probability that a taxi starting off_Downtown, will be Downtown after letting off its seventh fare?

The Taxi Problem A taxi company has divided the city into three regions - Northside, Downtown, and Southside. By keeping track of pickups and deliveries, the company has found that of the fares picked up in Northside, 50% stay in that region, 20% are taken Downtown, and 30% go to Southside. Of the fares picked up Downtown, only 10% go to Northside, 40% stay Downtown, and 50% go to Southside. Of the fares picked up in Southside, 30% go to each of Northside and Downtown, while 40% stay in Southside. We would like to know what the distribution of taxis will be over time as they pick up and drop off successive fares. Suppose we want to know the probability that a taxi starting off_Downtown, will be Downtown after letting off its seventh fare?

A First Course in Probability (10th Edition)
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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Subject: Discrete Structures
Topic: Probability

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The Taxi Problem A taxi company has divided the city into three regions - Northside, Downtown, and Southside. By keeping track of pickups and deliveries, the company has found that of the fares picked up in Northside, 50% stay in that region, 20% are taken Downtown, and 30% go to Southside. Of the fares picked up Downtown, only 10% go to Northside, 40% stay Downtown, and 50% go to Southside. Of the fares picked up in Southside, 30% go to each of Northside and Downtown, while 40% stay in Southside. We would like to know what the distribution of taxis will be over time as they pick up and drop off successive fares. Suppose we want to know the probability that a taxi starting off Downtown, will be Downtown after letting off its seventh fare? 0.4
Transcribed Image Text:The Taxi Problem A taxi company has divided the city into three regions - Northside, Downtown, and Southside. By keeping track of pickups and deliveries, the company has found that of the fares picked up in Northside, 50% stay in that region, 20% are taken Downtown, and 30% go to Southside. Of the fares picked up Downtown, only 10% go to Northside, 40% stay Downtown, and 50% go to Southside. Of the fares picked up in Southside, 30% go to each of Northside and Downtown, while 40% stay in Southside. We would like to know what the distribution of taxis will be over time as they pick up and drop off successive fares. Suppose we want to know the probability that a taxi starting off Downtown, will be Downtown after letting off its seventh fare? 0.4
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