33 1 Question 2.4 (SAFETY SAVES) To stay in touch with an airplane, an engineer

Question

33 1 Question 2.4 (SAFETY SAVES) To stay in touch with an airplane, an engineer designed a system that consists of four relays connected as shown in the following diagram: R2 Rs R4 Fig 2.4. Safety device Assume the relays Ri, Ra, Rj and Ra function independently. If the probabilities that the relays Ri, Ra, DGC ·32, DGOC80 3and R4 fail are: ,0.25 and 0.22, respectively. (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

a) Probability that the system 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 - 0.321)(1 - 0.2927) ) * ( 0.25*0.22)

= 0.9714

Therefore 0.9714 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 - 0.321)*(1 - 0.2927 ) / 0.9714

= 0.4944

Therefore 0.4944 is the required probability here.

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