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 I 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 sample space? [For example, if component I 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 w ill he probability of system function when component I doesn't work?

Explanation / Answer

a)

Possible out comes:-- (each of three could be filled in two ways : S or F ==> total possible cases = 2 x 2 x 2 = 8)

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

b) for system to function:-- we need

i ) there must be S for the switch 1

ii) either or both of the switches 2 and 3 should be S

So the successful cases are :-- SSS ; SSF ; SFS = 3 cases

c) probability for system functioning = successful cases / total cases = 3/8

When the component 1 doesnt work ==> the system wont function ==> probability = 0

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.