Three components are connected to form a system as shown in the accompanying dia

Question

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.

The experiment consists of determining the condition of each component [S (success) for a functioning component and F (failure) for a nonfunctioning component].

Possible outcomes:

(a) What outcomes are contained in the event A that exactly two of the three components function?

(b) What outcomes are contained in the event B that at least two of the components function?

(c) What outcomes are contained in the event C that the system functions?

(d) List outcomes in C'.

(e) List outcomes in A C.

(f) List outcomes in A C.

(g) List outcomes in B C.

(h) List outcomes in B C.

Explanation / Answer

A. Exactly 2 of the 3 components function are given by SSF, SFS and FSS

B. It will have SSF, SFS, FSS, and SSS

C. Component 1 should always be S and one out of the other two should be S. Thus answer is SSS, SSF, SFS

D. C' will be the event that is not contained in C. Thus it will.be FSS , SFF, FFS, and FFF

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