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

Reference:

Jay L. Devore, Probability and Statistics, For Engineering and The Sciences (Fifth Edtion)