an engineer designed a system that Question 2.4 (SAFETY SAVES) To stay in touch
ID: 3312531 • Letter: A
Question
an engineer designed a system that Question 2.4 (SAFETY SAVES) To stay in touch with an airplane, consists of four relays connected as shown in the following diagram: R: Rs R4 Fig 2.4. Safety device Assume the relays Ri, R2, Rs and Ra function independently. If the probabilities that the relays Ri, R3. Ro and Ra fail are: Doc+700 8 DGC .,0.25 and 0.22, respectively. , DOC-700 (a ) What is the probability that the system functions? (b) Given that the safety system worked when relays were activated, what is the probability that relays Ri and R2 functioned?Explanation / Answer
R1 fails = 445/(445+700) = 0.3886
R2 fails = 455/(445+800) = 0.3574
a) Probability that the system is functions is computed as:
= 1 - Probability that both subsystems R12, and R34 does not function
= 1 - Probability that R12 does not work*Probability that R34 does not work
= 1 - (1 - (1 - 0.3886)(1 - 0.3574) ) * ( 0.25*0.22)
= 0.9666
Therefore 0.9666 is the required probability here.
b) Now given that the sysmte works, probability that R12 works is computed as:
= Probability that R12 works and system works / Probability that system works
= (1 - 0.3886)*(1 - 0.2927 ) / 0.9666
= 0.4474
Therefore 0.4474 is the required probability here.
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