### Component System Probability Analysis**Figure Description:**The figure illustrates a system of four components connected in a specific configuration, depicted by four labeled boxes connected by lines. The components are as follows:- **Components 1 and 2**: These are connected in parallel. In a parallel configuration, the subsystem functions correctly if at least one of the components is working.- **Components 3 and 4**: These are connected in series. In a series configuration, the subsystem functions only if both components are working.**Task:**Calculate the probability that the entire system works correctly, given:- Each component operates independently.- The probability of any given component working is $ P(\text{component working}) = 0.9 $.**Solution Approach:**1. **Parallel Configuration (Components 1 and 2):** - Probability that either Component 1 or 2 works: - $ P(\text{at least one works}) = 1 - P(\text{neither work}) $ - $ P(\text{neither 1 nor 2 work}) = (1 - 0.9)(1 - 0.9) = 0.1 \times 0.1 = 0.01 $ - $ P(\text{at least one works}) = 1 - 0.01 = 0.99 $2. **Series Configuration (Components 3 and 4):** - Probability that both Component 3 and 4 work: - $ P(\text{both work}) = P(\text{3 works}) \times P(\text{4 works}) = 0.9 \times 0.9 = 0.81 $3. **Entire System:** - Final probability that the entire system functions is the product of the probabilities of each subsystem functioning: - $ P(\text{system works}) = P(\text{1 and 2 parallel}) \times P(\text{3 and 4 series}) = 0.99 \times 0.81 = 0.8019 $Therefore, the probability that the entire system works correctly is **0.8019**.

We can divide the system in two parts.Parallel subsystem works (if either 1 or 2 work).Series…

Answered: Components 1 and 2 are connected in…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Assume the chances of failure of each component is given in Figure. What is the probability that the system would not work? .
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