Homework Help is Here – Start Your Trial Now!
Math
Probability
Consider the system of independent components connected as in the figure below. The system works only if there is a path of functional components from left to right. Components 1 and 2 are connected in parallel, so that subsystem works if and only if either 1 or 2 works. Since 3 and 4 are connected in series, that subsystem works if and only if both 3 and 4 work. Suppose that P(1 works) = 0.73, P(2 works) = 0.76, P(3 works) = 0.83, and P(4 works) = 0.87, and these events are mutually independent. 1 2 (a) Find the probability that the system works. (b) Find the probability that component 1 works, given that the system works.

Consider the system of independent components connected as in the figure below. The system works only if there is a path of functional components from left to right. Components 1 and 2 are connected in parallel, so that subsystem works if and only if either 1 or 2 works. Since 3 and 4 are connected in series, that subsystem works if and only if both 3 and 4 work. Suppose that P(1 works) = 0.73, P(2 works) = 0.76, P(3 works) = 0.83, and P(4 works) = 0.87, and these events are mutually independent. 1 2 (a) Find the probability that the system works. (b) Find the probability that component 1 works, given that the system works.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 24EQ: Suppose the coal and steel industries form a closed economy. Every $1 produced by the coal industry...
See similar textbooks
Question
Consider the system of independent components connected as in the figure below. The system works only if there is a path of functional components from left to right. Components 1 and 2 are connected in parallel, so that subsystem works if and only if either 1 or 2 works. Since 3 and 4 are connected in series, that subsystem works if and only if both 3 and 4 work. Suppose that P(1 works) = 0.73, P(2 works) = 0.76, P(3 works) = 0.83, and P(4 works) = 0.87, and these events are mutually independent. 1 2 (a) Find the probability that the system works. (b) Find the probability that component 1 works, given that the system works.
Transcribed Image Text:Consider the system of independent components connected as in the figure below. The system works only if there is a path of functional components from left to right. Components 1 and 2 are connected in parallel, so that subsystem works if and only if either 1 or 2 works. Since 3 and 4 are connected in series, that subsystem works if and only if both 3 and 4 work. Suppose that P(1 works) = 0.73, P(2 works) = 0.76, P(3 works) = 0.83, and P(4 works) = 0.87, and these events are mutually independent. 1 2 (a) Find the probability that the system works. (b) Find the probability that component 1 works, given that the system works.
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer