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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. Which outcomes are contained in the event A that exactly 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 CÊ¹, A ˆª C, A ˆ© C, B ˆª C, and B ˆ© C.

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