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...

See similar textbooks

Related questions

Q: To generate leads for new business, Gustin Investment Services offers free financial planning…

A: From the given information ,Total number of trials , n = 25 Each seminar costs Gustin = $3900the…

Q: There are exactly 365 students taking math class this semester. Assume that each of these students…

A: We have given that There are exactly 365 students taking math class this semester. Assume that each…

Q: Suppose that 85% of all defendants are indeed guilty. In a criminal trial by jury, the probability…

A: Let A1, A2, ... , An be n mutually exclusive and exhaustive events with P(Ai) > 0 for all i = 1,…

Q: If you are choosing one state at random, are you more likely to choose a state whose name begins…

A: One state is chosen at random. The objective is to determine whether you are more likely to choose…

Q: Based on a study from the Chronicles of Flippin'' Awesomeness, the probability that Napoleon and…

Q: A piece of equipment will function only when the three components A, B and C are working. The…

A: Given: A piece of equipment will function only when the three components A, B and C are working.…

Q: In a population of 10,000, there are 5000 nonsmokers, 2500 smokers of one pack or less per day, and…

A: Given Information: In a population of 10,000, there are 5000 smokers, 2500 smokers of one pack or…

Q: What is the probability that Kylo passes the accounting test? (ii.) Given that Kylo passes the…

A: Kylo’s accounting skills can be categorized as Good, Fair, or Poor, each with equal probability.…

Q: Based on a study from the Chronicles of Flippin'' Awesomeness, the probability that Napoleon and…

Q: Suppose that an employee at a local company checks his watch and realizes that he has 10 minutes to…

A: Multiplication rule for independent events:If two events A and B are independent then the…

Q: Based on a study from the Chronicles of Flippin'' Awesomeness, the probability that Napoleon and…

A: Giventhe probability that Napoleon and Pedro make it to their first period class on time = 0.46The…

Q: Assume that there are 15 board members: 10 females, and 5 males including Joe. There are 2 tasks to…

A: Given information: According to the given information, the total number of board members is n(S) =…

Q: 4. Teddy lives life on the edge and gets dressed randomly every morning. This morning, he is…

A: Number of black shoes is 2. Number of brown shoes is 3. Number of black pant is 3. Number of brown…

Q: per day. For smokers who smoke a pack or less per day, there is a 10% probability of quitting and a…

Q: What is the probability that Napoleon and Pedro catch the bus and make it to their first period…

Q: In a population of 10,000, there are 5000 nonsmokers, 2500 smokers of one pack or less per day, and…

A: The given Information can be depicted as follows: During any month Begin smoking 1…

Q: In a population of 10,000, there are 5000 nonsmokers, 2500 smokers of one pack or less per day, and…

A: Given, Total population : 10000 Nonsmokers : 5000 Smokers of one pack or less per day : 2500…

Q: Kristina is the general manager for a business. One of Kristina's tasks is to assign extra projects…

A: Errors do happen though. Kristina makes an error once every 59 tasks that she assigns.

Q: Assume that at the airport security check, 60% of all passengers are selected for a random bag…

A: Given that p = 60% = 0.60 n = 10 X ~Binomial(n, p) X ~ Binomial (10, 0.60)The PMF of the Binomial…

Q: An insurer writes a large book of home warranty policies. You are given the following information…

Q: The best free throw shooter in NBA history is Stephen Curry who has made 91% of his free throw…

A: Let be the number of number of free throws.The probability of making free shot: The total number…

Q: What conclusions could you make about the three mistakes? Make sure to explain your conclusion…

A: Answer:----:. Date:----4/10/2021

Q: The graph shown in the image depicts the market for a subscription toEconomics Todaymagazine. Up to…

A: From the graph it is concluded that the demand at price $4 is equal to 12. But according to the…

Q: In a population of 10,000, there are 5000 nonsmokers, 2500 smokers of one pack or less per day, and…

A: The given transition matrix in this case is Non-smokers Smokers 1 pack per day or less Smokers…

Q: Assuming that these two are Independent, what is the probability of thunderstorms on both Memorial…

A: Concept: If the probability of occurrence of one event is not affected by the probability of…

Q: In a population of 10,000, there are 5000 nonsmokers, 2500 smokers of one pack or less per day, and…

A: The number of non-smokersThe number of smokers of one pack or less per dayThe number of smokers of…

Q: Suppose a free throw shooter makes 67 percent of their first attempts. On the second attempt they…

Q: Illustration 66. 50 out of every 1000 cigarettes are rolled up in gold flake and are mixed with the…

Q: The problem of traffic delay in a highway can be studied in the following way. Let us assume that…

Q: In each trial of an experiment, an error occurs with probability 0.15. An error is a major error…

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?

Video Video

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1: Given that,

VIEW

Step 2: (a) Probability that all 4 servers have the same maintenance day:

VIEW

Step 3: (b) Probability that each server has a distinct maintenance day

VIEW

Step 4: (c) Probability that at least 2 servers have the same maintenance day

VIEW

Solution

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 5 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Numerical$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.

Similar questions

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:
In a town, there are three bridges: Bridge A, Bridge B, and Bridge C. On any given day, the probability of each bridge being open for passage is as follows: P(A) = 0.4, P(B) = 0.3, and P(C) = 0.5. If a resident needs to cross all three bridges in succession, what is the probability of successfully crossing all three bridges without encountering any closures?
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?
The three-year recidivism rate of parolees in a certain state is about 20%; that is, 20% of parolees end up back in prison within three years. Assume that whether one parolee returns to prison is independent of whether any of the others return. Complete parts a and b below. Find the probability that exactly 6 out of 20 parolees will end up back in prison within three years. The probability that exactly 6 out of 20 parolees will end up back in prison is nothing.
The genotype of an organism can be either normal (wild type, W) or mutant (M). Each generation, a wild type individual has probability 0.03 of having a mutant offspring, and a mutant has probability 0.005 of having a wild type offspring.
On average a certain intersection results in 3 traffic accidents per month. What is the probability that for any given month at this intersection: 5 or 6 accidents in half of a year?
Brgy. Pallet has one Full Restore and one Max Revive available for emergencies. The probability that the Full Restore is available for use is 0.98 and the probability that the Max Revive is available for use is 0.92. Assuming that the availability of these items is independent of each other, what is the probability that both of these items are available for a Trainer to use?
Based on a study from the Chronicles of Flippin'' Awesomeness, the probability that Napoleon and Pedro make it to their first period class on time is 0.37. The probability that Napoleon and Pedro catch the bus is 0.66. However, the probability that they make it to their first period class on time, given that they catch the bus is 0.61. What is the probability that Napoleon and Pedro catch the bus and make it to their first period class on time?
A local company has two identical lathe machines which are operated independently. A log is kept for each of the two machines and Table QII below shows the number of times that each machine has been operational in the last twelve months. Lathe Status Number of times working Number of times not working A B 780 650 220 350 Table QII Draw the probability tree diagram and solve following questions Q1 If two machines are dependent what is the probability of either lathe working at the visit of supervisor? Q2 What is the probability that only one lathe would broke down? Q3 What is the probability that at least one lathe would have broken down ?
Jack has just been given a ten-question multiple choice quiz in history class. Each question has five answers, of which only one is correct. Since Jack has not attended class recently, he does not know any of the answers. Assuming Jack guesses randomly on all ten questions, find the probability that he will answer six or more of the questions correctly and avoid an F.
Based on a study from the Chronicles of Flippin'' Awesomeness, the probability that Napoleon and Pedro make it to their first period class on time is 0.29. The probability that Napoleon and Pedro catch the bus is 0.87. However, the probability that they make it to their first period class on time, given that they catch the bus is 0.81. What is the probability that Napoleon and Pedro catch the bus and make it to their first period class on time?
Please provide steps for how you got the solution to the problem provided below. A machine is used to produce one of each of two types of product (A and B) on alternating days, i.e., if A is produced today then B will be produced tomorrow and vice versa. Each day, there is a probability that the machine malfunctions. Malfunction probability after a day of operation is 0.03 when producing A and 0.07 when producing B. Once the machine malfunctions, it is no longer operable and will not be replaced until sometime in the future (beyond modeling horizon). Model the system as a Markov chain (give transition matrix on your paper). Suppose that on Monday product A was produced. Find the probability that the machine is still operable by the morning of Thursday. Your model should have a state ”malfunction”, which cannot transition to any other state other than itself.