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. (View Pic)
The experiment consists of determining the condition of each component [S (success) for a functioning component andF (failure) for a nonfunctioning component]. (Enter your answers in set notation. Enter EMPTY or ∅ for the empty set.)
(a) Which outcomes are contained in the eventA that exactly two of the three components function?
A
= ?
(b) Which outcomes are contained in the eventB that at least two of the components function?
B
= ?
(c) Which outcomes are contained in the eventC that the system functions?
C
= ?
(d) List outcomes inC'.
C'
= ?
List outcomes inA ∪C.
A ∪C
= ?
List outcomes inA ∩C.
A ∩C
= ?
List outcomes inB ∪C.
B ∪C
= ?
List outcomes inB ∩C.
B ∩C
= ?
Extracted text: 2 3.