A communication network consists of five links that interconnect four routers, as shownbelow. The probability that each of the link is operational is and independent. What isthe probability of being able to transmit a message from router A to router B (assume thatpackets move forward in the direction of the destination))?

Given: To find: The possible paths.

Answered: A communication network consists of…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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When Mitchell drives back home from campus, he has to pass through two sets of traffic lights. The probability that he has to stop at the first is 0.33, while the probability he has to stop at the second set is 0.41. Also, the probability he does not have to stop at either traffic light is 0.31. What is the probability he has to stop at exactly one set of traffic lights?
Two boxes each contain long and short bolts. Box 1 contains 60 long and 40 short bolts, while box 2 contains 10 long and 20 short bolts. One box is selected at random and one bolt is then chosen from the selected box. a. Find the probability the chosen bolt is long. b. Given that the chosen bolt was long, find the probability that box 1 was selected.
Of the cartons produced by a company, 5% have a puncture, 6% have a smashed comer, and 0.4% have both a puncture and a smashed corner. Find the probability that a randomly selected carton has a puncture or a smashed comer. The probability that a randomly selected carton has a puncture or a smashed corner (Type an integer or a decimal. Do not round.) %.
A person randomly selects one of six envelopes. Each envelope contains a check that the person gets to keep. Determine the person's expectation if three envelopes contain a $486 check and three envelopes contain a $987 check.
Each of the letters a through j are printed o tiles then placed in a hat. Andre selects a tile at random and then replaces it. Clare also selects a tile at random. What is the probability that Andre and Clare both select tile b?
Industrial Robots are programmed to operate through microprocessors. The probability that one such computerized robot breaks down during any one 8-hour shift is 0.2. Find the probability that the robot will operate for at most five shifts before breaking down twice.
Of the cartons produced by a company, 10% have a puncture, 5% have a smashed corner, and 0.9% have both a puncture and a smashed corner. Find the probability that a randomly selected carton has a puncture or a smashed corner. The probability that a randomly selected carton has a puncture or a smashed corner (Type an integer or a decimal. Do not round.)
Of the cartons produced by a company, 10% have a puncture, 4% have a smashed corner, and 1.3% have both a puncture and a smashed corner. Find the probability that a randomly selected carton has a puncture or a smashed corner. The probability that a randomly selected carton has a puncture or a smashed corner (Type an integer or a decimal. Do not round.) %.
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.
Machines A and B produce 40% and 60% respectively of the production of a component intended for the motor industry. The probability that machine A produces a defective component is 0.05 while the probability that machine B produces a defective component is 0.09.D. If a component is selected at random and is found to be not defective, find the probability that it was made by machine B.E. What is the probability to find a component that is not defective and it was made by machine A?F. What is the probability to find a component that is not defective and it was made by machine B?

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