Suppose that Art can decide to go to work by one of three modes of transportation, car, bus, or commuter train. Because of high traffic, if he decides to go by car, there is a 60% chance he will be late. If he goes by bus, which has special reserved lanes but is sometimes overcrowded, the probability of being late is only 20%. The commuter train is almost never late, with a probability of only 2%, but is more expensive than the bus. Suppose that Art is late one day, and his boss wishes to estimate the probability that he drove to work that day by car. Since he does not know which mode of transportation Art usually uses, he gives a prior probability of 1/3 to each of the three possibilities. • What is the boss' estimate of the probability that Art drove to work? • Suppose that a coworker of Art's knows that he almost always takes the commuter train to work, never takes the bus, but sometimes, 20% of the time takes the car. What is the co-worker's probability that Art drove to work that day, given that he was late?
Suppose that Art can decide to go to work by one of three modes of transportation, car, bus, or commuter train. Because of high traffic, if he decides to go by car, there is a 60% chance he will be late. If he goes by bus, which has special reserved lanes but is sometimes overcrowded, the probability of being late is only 20%. The commuter train is almost never late, with a probability of only 2%, but is more expensive than the bus. Suppose that Art is late one day, and his boss wishes to estimate the probability that he drove to work that day by car. Since he does not know which mode of transportation Art usually uses, he gives a prior probability of 1/3 to each of the three possibilities. • What is the boss' estimate of the probability that Art drove to work? • Suppose that a coworker of Art's knows that he almost always takes the commuter train to work, never takes the bus, but sometimes, 20% of the time takes the car. What is the co-worker's probability that Art drove to work that day, given that he was late?
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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Transcribed Image Text:Suppose that Art can decide to go to work by one of three modes of transportation, car, bus, or
commuter train. Because of high traffic, if he decides to go by car, there is a 60% chance he will be
late. If he goes by bus, which has special reserved lanes but is sometimes overcrowded, the probability
of being late is only 20%. The commuter train is almost never late, with a probability of only 2%, but
is more expensive than the bus.
Suppose that Art is late one day, and his boss wishes to estimate the probability that he drove to work
that day by car. Since he does not know which mode of transportation Art usually uses, he gives a
prior probability of 1/3 to each of the three possibilities.
What is the boss' estimate of the probability that Art drove to work?
Suppose that a coworker of Art's knows that he almost always takes the commuter train to
work, never takes the bus, but sometimes, 20% of the time takes the car. What is the co-worker's
probability that Art drove to work that day, given that he was late?
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