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 and F (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 event A that exactly two of the three components function? A = ? (b) Which outcomes are contained in the event B that at least two of the components function? B = ? (c) Which outcomes are contained in the event C that the system functions? C = ? (d) List outcomes in C'. C' = ? List outcomes in A ∪ C. A ∪ C = ? List outcomes in A ∩ C. A ∩ C = ? List outcomes in B ∪ C. B ∪ C = ? List outcomes in B ∩ C. B ∩ C = ?
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
The experiment consists of determining the condition of each component [S (success) for a functioning component and F (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
A = ?
(b) Which outcomes are contained in the event B that at least two of the components function?
B = ?
(c) Which outcomes are contained in the event C that the system functions?
C = ?
(d) List outcomes in C'.
C' = ?
List outcomes in A ∪ C.
A ∪ C = ?
List outcomes in A ∩ C.
A ∩ C = ?
List outcomes in B ∪ C.
B ∪ C = ?
List outcomes in B ∩ C.
B ∩ C = ?
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