Three components are connected to form a system as shown in the accompanying dia

Question

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 [5 (success) for a functioning component and F (failure) for a nonfunctioning component]. (a) Which outcomes are contained in the sample space? [For example, if component 1 works but 2 and 3 don't then event is represented as SFF, which such events are in the sample space?] b) Which outcomes are contained in the event that the system functions? (c) Find the probability that the system functions. What will be probability of system function when component 1 doesn't work?

Explanation / Answer

a)

possible outcomes are

{ SSS, SSF, SFS , SFF , FSS, FFS,FSF,FFF }

b)

the possible outcomes are

{ SSS,SSF,SFS }

c)

probability that system functions = 3/9 = 1/3

probability that system functions when 1 doesnt work = 0

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