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

Solution: Step 1: Given that a system that consist of 2 subsystems. Here the components in the 2–3 subsystem are connected in parallel so the system will function if and only if component one and at least one of two(2-3) individual component functions . Step 2: a) Here the event A is defined as that exactly two out three components in the system is functions. So it is clear that the outcomes of this event will be 1) (1,2) (component one and two functions) 2) (1,3) 3) (2,3) b) Since the event B is defined as that at least two of three components function the outcomes of the event will be. 1) (1,2) 2) (1,3) 3) (2,3) 4) (1,2,3) (all the components functions in the system)