You arrive at CS109 Office Hours to find that 5 CS109 CAs—Yonatan, Will, Kathleen, Jacob, and Naomi—are all present, and each is working with some fellow CS109 student of yours. You notice there are nine other students in front of you in the queue and no one is behind you. It looks like you'll be the last of 10 students to be helped. We'll assume the time each CA spends with a student can be modeled as an Exponential random variable such that, on average, each CA finishes helping precisely 6 students every hour. As a CA finishes helping a student, they immediately start helping the next student in line and remove them from the queue. Question: What's the probability that you are the last student to actually leave office hours? Assume each student leaves office hours as soon as the CA has finished helping them. Present your probability to two decimal places.
You arrive at CS109 Office Hours to find that 5 CS109 CAs—Yonatan, Will, Kathleen, Jacob, and Naomi—are all present, and each is working with some fellow CS109 student of yours. You notice there are nine other students in front of you in the queue and no one is behind you. It looks like you'll be the last of 10 students to be helped. We'll assume the time each CA spends with a student can be modeled as an Exponential random variable such that, on average, each CA finishes helping precisely 6 students every hour. As a CA finishes helping a student, they immediately start helping the next student in line and remove them from the queue. Question: What's the probability that you are the last student to actually leave office hours? Assume each student leaves office hours as soon as the CA has finished helping them. Present your probability to two decimal places.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter10: Matrices
Section10.1: Solution Of Linear Systems
Problem 56E
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Question
You arrive at CS109 Office Hours to find that 5 CS109 CAs—Yonatan, Will, Kathleen, Jacob, and Naomi—are all present, and each is working with some fellow CS109 student of yours. You notice there are nine other students in front of you in the queue and no one is behind you. It looks like you'll be the last of 10 students to be helped.
We'll assume the time each CA spends with a student can be modeled as an Exponential random variable such that, on average, each CA finishes helping precisely 6 students every hour. As a CA finishes helping a student, they immediately start helping the next student in line and remove them from the queue.
Question: What's the probability that you are the last student to actually leave office hours? Assume each student leaves office hours as soon as the CA has finished helping them. Present your probability to two decimal places.
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