4. An electrical system consists of identical components that are operational with probability pindependently of other components. The components are connected in three subsystems, asshown in the Figure 1. The system is operational if there is a path that starts at point A,ends at point B, and consists of operational components. This is the same as requiring thatall three subsystems are operational. What are the probabilities that the three subsystems,as well as the entire system, are operational?ВFigure 1: A system of identical components that consists of the three subsystems 1, 2, and 3. The system isoperational if there is a path that starts at point A, ends at point B, and consists of operational components.

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Answered: 4. An electrical system consists of…

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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Two people, A and B, are competing for the control of a corporation. The probabilities that these two people will win are 0.7 and 0.3, respectively. If A wins, the probability of introducing a new product is 0.8; if B wins, the corresponding probability is 0.4. a) What is the probability that a new product will be introduced? b) If a new product is introduced, what is the probability that B won the competition?
A certain system can experience three different types of defects. Let Ai (i = 1,2,3) denote the event that the system has a defect of type i. Suppose that the following probabilities are true. P(A1) = 0.10 P(A2) = 0.07 P(A3) = 0.06P(A1 ∪ A2) = 0.11 P(A1 ∪ A3) = 0.13P(A2 ∪ A3) = 0.11 P(A1 ∩ A2 ∩ A3) = 0.01 (c) Given that the system has at least one type of defect, what is the probability that it has exactly one type of defect? (Round your answer to four decimal places.) (d) Given that the system has both of the first two types of defects, what is the probability that it does not have the third type of defect? (Round your answer to four decimal places.)
A system has six components connected as shown in the following diagram: A Assume A, B, C, D, E, and F function independently. If the probabilities that A, B, C, D, E, and F fail are 0.01, 0.05, 0.02, 0.08, 0.10, and 0.05 respectively, what is the probability that the system fails?
A machine has four components, A, B, C, and D, set up in such a manner that all four parts must work for the machine to work properly. Assume the probability of one part working does not depend on the functionality of any of the other parts. Also assume that the probabilities of the individual parts working are P(A) = P(B) = 0.95, P(C) = 0.91, and P(D) = 0.96. Find the probability that at least one of the four parts will work. Round to six decimal places.
1. The picture's river has floodgates at points A, B, C and D. The probabilities of each of the floodgates being open (a requirement for water to pass through) are the following: A: 94%, B : 96%, C: 91%, D: 97% The probabilities of the floodgates being open are independent. What is the probability that the water from the leftmost point in the picture will reach the sea on the right? C D B THE SEAL

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