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].

(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'.

List outcomes in A C.

List outcomes in A C.

List outcomes in B C.

List outcomes in B C.

SSS SSF SFS FSS FF SFF FSF FFS FFF SS

Explanation / Answer

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

Total outcomes are

SS

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

Event A : Exactly two of the three components function.

A={SSF, SFS, FSS}

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

Event B : At least two of the components function.

B = {SSF,SFS,FSS,SSS}

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

Event C : The system functions.

C={SSF, SFS, FSS, SSS}

(d) List outcomes in C'.

C' ={ FF,SFF,FSF,FFS,FFF,SS}

List outcomes in A C = {SSF, SFS, FSS, SSS}

List outcomes in A C = {SSF, SFS, FSS}

List outcomes in B C = {SSF, SFS, FSS, SSS}

List outcomes in B C = {SSF, SFS, FSS, SSS}

SSS SSF SFS FSS FF SFF FSF FFS FFF

SS

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