The time that it takes to service a car is an exponential random variable with rate 1. 1. If A brings his car in at time 0 and B brings his car in at time t, what is the probability that B’s car is ready before A’s? Assume that the service times are independent, and the service begins upon arrival. 2. If both cars are brought in at time 0, with work starting on B’s car only when A’s car has been completely serviced, what is the probability that B’s car is ready before 2?

The time that it takes to service a car is an exponential random variable with rate 1. 1. If A brings his car in at time 0 and B brings his car in at time t, what is the probability that B’s car is ready before A’s? Assume that the service times are independent, and the service begins upon arrival. 2. If both cars are brought in at time 0, with work starting on B’s car only when A’s car has been completely serviced, what is the probability that B’s car is ready before 2?

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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Question

The time that it takes to service a car is an exponential random variable with rate 1.
1. If A brings his car in at time 0 and B brings his car in at time t, what is the probability that
B’s car is ready before A’s? Assume that the service times are independent, and the service
begins upon arrival.
2. If both cars are brought in at time 0, with work starting on B’s car only when A’s car has been
completely serviced, what is the probability that B’s car is ready before 2?

Detailed explanation and calculation would be much appreciated.

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