Three components are connected to form a system as shown in the accompanying diagram. Because the components in the 2–3 subsystem are connected in parallel, that subsystem will function if at least one of the two individual components functions. For the entire system to function, component 1 must function and so must the 2–3 subsystem |-------2-------| ---1------>| |----------> |-------3-------| The experiment consists of determining the condition of each component [S(success) for a functioning component and F(failure) for a nonfunctioning component]. a. Which outcomes are contained in the event A that exactly two out of the three components function? b. Which outcomes are contained in the event B that at least two of the components function? c. Which outcomes are contained in the event C that the system functions? d. List outcomes in C', A U C, B U C.
Three components are connected to form a system as shown in the accompanying diagram. Because the components in the 2–3 subsystem are connected in parallel, that subsystem will function if at least one of the two individual components functions. For the entire system to function, component 1 must function and so must the 2–3 subsystem |-------2-------| ---1------>| |----------> |-------3-------| The experiment consists of determining the condition of each component [S(success) for a functioning component and F(failure) for a nonfunctioning component]. a. Which outcomes are contained in the event A that exactly two out of the three components function? b. Which outcomes are contained in the event B that at least two of the components function? c. Which outcomes are contained in the event C that the system functions? d. List outcomes in C', A U C, B U C.
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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Three components are connected to form a system as shown
in the accompanying diagram. Because the components in
the 2–3 subsystem are connected in parallel, that subsystem
will function if at least one of the two individual components
functions . For the entire system to function, component 1
must function and so must the 2–3 subsystem
|-------2-------|
---1------>| |---------->
|-------3-------|
The experiment consists of determining the condition of each
component [S(success) for a functioning component and
F(failure) for a nonfunctioning component].
a. Which outcomes are contained in the event A that exactly
two out of the three components function?
b. Which outcomes are contained in the event B that at least two of the components function?
c. Which outcomes are contained in the event C that the system functions?
d. List outcomes in C', A U C, B U C.
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