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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.

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 out 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 $C^{\prime}, A \cup C, A \cap C, B \cup C,$ and $B \cap C$ .

(a) A ={SSF, SFS, FSS} $\\$

(b) B ={SSS, SSF, SFS, SSS} $\\$

(c) C ={SSS, SSF, SFS}$\\$

(d) C0 ={SFF, FSS, FSF, FFS, FFF}

A [ C ={SSS, SSF, SFS, FSS}

A \ C ={SSF, SFS}

B [ C ={SSS, SSF, SFS, FSS}

B \ C ={SSS, SSF, SFS}

Probability Topics

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