Three components are connected to form a system asshown in the accompanying diagram

Chapter 2, Problem 3

(choose chapter or problem)

Three components are connected to form a system as shown in the accompanying diagram. Because the components of the 23 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. Which outcomes are contained in the event A thatexactly two out of the three components function?

b. Which outcomes are contained in the event B that at least two of the components function?

c. Which 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 \(B \cup C\)

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