Consider the situation that we have 4 servers, each of which needs to be down for one day (a particular date, NOT a rolling window of 24 hours) for maintenance. Suppose that for each server, we randomly select a day in April (which has 30 days) as the maintenance day. Answer the following questions: (a) What's the probability that all 4 servers have the same maintenance day? (b) What's the probability that each server has a distinct maintenance day? (c) What's the probability that at least 2 servers have the same maintenance day?

Consider the situation that we have 4 servers, each of which needs to be down for one day (a particular date, NOT a rolling window of 24 hours) for maintenance. Suppose that for each server, we randomly select a day in April (which has 30 days) as the maintenance day. Answer the following questions: (a) What's the probability that all 4 servers have the same maintenance day? (b) What's the probability that each server has a distinct maintenance day? (c) What's the probability that at least 2 servers have the same maintenance day?

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

Consider the situation that we have 4 servers, each of which needs to be down for one
day (a particular date, NOT a rolling window of 24 hours) for maintenance. Suppose
that for each server, we randomly select a day in April (which has 30 days) as the
maintenance day. Answer the following questions:
(a) What's the probability that all 4 servers have the same maintenance day?
(b) What's the probability that each server has a distinct maintenance day?
(c) What's the probability that at least 2 servers have the same maintenance day?

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In a population of 10,000, there are 5000 nonsmokers, 2500 smokers of one pack or less per day, and 2500 smokers of more than one pack per day. During any month, there is a 5% probability that a nonsmoker will begin smoking a pack or less per day, and a 4% probability that a nonsmoker will begin smoking more than a pack per day. For smokers who smoke a pack or less per day, there is a 10% probability of quitting and a 10% probability of increasing to more than a pack per day. For smokers who smoke more than a pack per day, there is a 9% probability of quitting and a 10% probability of dropping to a pack or less per day. How many people will be in each group in 1 month, in 2 months, and in 1 year? (Round your answers to the nearest whole number.)(a) in 1 month:nonsmokers:1 pack/day or less:more than 1 pack/day:(b) in 2 months:nonsmokers:1 pack/day or less:more than 1 pack/day:(c) in 1 year:nonsmokers:1 pack/day or less:more than 1 pack/day:
Solve the following probabilty problem: Doris and her friend plan to travel to Florida during the winter intersession period. Based upon the past experience they know that the probability that they go by car is 0.4 and the probability that they go by plane is 0.2. What is the probability that they travel to Florida by car or plane only?
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