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Assume that the number of bikes arriving at the campus follows a Poisson process with a rate of 200 per hour. Out of those bikes, 5% are red and 95% have other colors. (i) What is the probability that 20 red bikes arrive within an hour? (ii) What is the probability that 20 red bikes arrive within the first hour and 500 bikes (of any color) arrive within the first three hours? (iii) Given that 20 red bikes arrived within an hour, what is the expected total number of bikes that arrived within this hour? (iv) Given that 150 bikes arrived within an hour, what is the probability that exactly 10 out of the

Assume that the number of bikes arriving at the campus follows a Poisson process with a rate of 200 per hour. Out of those bikes, 5% are red and 95% have other colors. (i) What is the probability that 20 red bikes arrive within an hour? (ii) What is the probability that 20 red bikes arrive within the first hour and 500 bikes (of any color) arrive within the first three hours? (iii) Given that 20 red bikes arrived within an hour, what is the expected total number of bikes that arrived within this hour? (iv) Given that 150 bikes arrived within an hour, what is the probability that exactly 10 out of the

College Algebra
College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 11ECP: A manufacturer has determined that a machine averages one faulty unit for every 500 it produces....
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Assume that the number of bikes arriving at the campus follows a Poisson process with a rate of 200 per hour. Out of those bikes, 5% are red and 95% have other colors. (i) What is the probability that 20 red bikes arrive within an hour? (ii) What is the probability that 20 red bikes arrive within the first hour and 500 bikes (of any color) arrive within the first three hours? (iii) Given that 20 red bikes arrived within an hour, what is the expected total number of bikes that arrived within this hour? (iv) Given that 150 bikes arrived within an hour, what is the probability that exactly 10 out of them were red?
Transcribed Image Text:Assume that the number of bikes arriving at the campus follows a Poisson process with a rate of 200 per hour. Out of those bikes, 5% are red and 95% have other colors. (i) What is the probability that 20 red bikes arrive within an hour? (ii) What is the probability that 20 red bikes arrive within the first hour and 500 bikes (of any color) arrive within the first three hours? (iii) Given that 20 red bikes arrived within an hour, what is the expected total number of bikes that arrived within this hour? (iv) Given that 150 bikes arrived within an hour, what is the probability that exactly 10 out of them were red?
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