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A system is composed of 5 components, each of which is
Chapter 2, Problem 5P(choose chapter or problem)
Problem 5P
A system is composed of 5 components, each of which is either working or failed. Consider an experiment that consists of observing the status of each component, and let the outcome of the experiment be given by the vector (x1,x2,x3, x4, x5), where xi is equal to 1 if component i is working and is equal to 0 if component i is failed.
(a) How many outcomes are in the sample space of this experiment?
(b) Suppose that the system will work if components 1 and 2 are both working, or if components 3 and 4 are both working, or if components 1, 3, and 5 are all working. Let W be the event that the system will work. Specify all the outcomes in W.
(c) Let A be the event that components 4 and 5 are both failed. How many outcomes are contained in the event A?
(d) Write out all the outcomes in the event AW.
Questions & Answers
QUESTION:
Problem 5P
A system is composed of 5 components, each of which is either working or failed. Consider an experiment that consists of observing the status of each component, and let the outcome of the experiment be given by the vector (x1,x2,x3, x4, x5), where xi is equal to 1 if component i is working and is equal to 0 if component i is failed.
(a) How many outcomes are in the sample space of this experiment?
(b) Suppose that the system will work if components 1 and 2 are both working, or if components 3 and 4 are both working, or if components 1, 3, and 5 are all working. Let W be the event that the system will work. Specify all the outcomes in W.
(c) Let A be the event that components 4 and 5 are both failed. How many outcomes are contained in the event A?
(d) Write out all the outcomes in the event AW.
ANSWER:
Step 1 of 5
From the given problem we have A system is composed of 5 components, each of which is either working or failed. And the outcome of the experiment be given by the vector
Where,
\(x_{i}=\left\{\begin{array}{l}1, \text { if component } i \text { is working } \\0, \quad \text { if component } i \text { is failed }\end{array}\right.\)
Here our goal is:
a). How many outcomes are in the sample space of this experiment.
b). We need to specify all the outcomes in W.
c). We need to find how many outcomes are contained in the event A.
d). We need to Write out all the outcomes in the event AW.