Question 2 (TRAFFIC LIGHTS ARE FOR YOUR SAFETY) An engineer designed a traffic l

Question

Question 2 (TRAFFIC LIGHTS ARE FOR YOUR SAFETY) An engineer designed a traffic light by using three selectors: S, S, and S He decided o use twe selectors Sy and S2 in series and the third selector S in parallel so that the sysen wuld sill work if either selector Sy or both selectors Sy and S work together All the three selectors work independently, Results showed that selectors S, 82, and S worked m 70% 75% and 65% of cases, respectively Traffic Signal Fig. Traffic rules are for our safety ( a ) What is the chance of the signal system failing? (b ) Assume the system worked; what is the conditional probability that selector S

Explanation / Answer

P(S1 Working) = 0.70 Thus, P(S1 fail) = 0.30

P(S2 Working) = 0.75 Thus, P(S2 fail) = 0.25

P(S3 Working) = 0.65 Thus, P(S3 fail) = 0.35

S1 & S2 are in series, S3 is in parallel

a)Cases when signal system fails

= S1,S2,S3 all fails + S2,S3 fails S1 Works+ S1,S3 fails S2 Works

= 0.30*0.25*0.35 + 0.70*0.25*0.35 + 0.30*0.75*0.35

= 0.16625

b) P(3 worked when system worked) =

{P (S1,S2,S3 worked) + P(S3 worked S1,S2 failed)} /{P(S1,S2 worked S3 failed)+ P (S1,S2,S3 worked) + P(S3 worked S1,S2 failed)}

= {{0.7*0.75*0.65} + (0.3*0.25*0.65)} / {(0.7*0.75*0.35) + {0.7*0.75*0.65} + (0.3*0.25*0.65)}

= 0.39 / 0.57375

= 0.68

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