Problem 1) A series of 20 jobs arrive at a computing center with 50 processors. Assume that each of the jobs is equally likely to go through any of the processors. a) Find the probability that a processor is used at least twice. b) What is the probability that at least one processor is idle? c) If any processor can handle at most four jobs without being overloaded, what is the probability of an overload?

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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### Problem 1

A series of 20 jobs arrive at a computing center with 50 processors. Assume that each of the jobs is equally likely to go through any of the processors.

a) **Find the probability that a processor is used at least twice.**

b) **What is the probability that at least one processor is idle?**

c) **If any processor can handle at most four jobs without being overloaded, what is the probability of an overload?**
Transcribed Image Text:### Problem 1 A series of 20 jobs arrive at a computing center with 50 processors. Assume that each of the jobs is equally likely to go through any of the processors. a) **Find the probability that a processor is used at least twice.** b) **What is the probability that at least one processor is idle?** c) **If any processor can handle at most four jobs without being overloaded, what is the probability of an overload?**
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