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

a) probability of system failing = (1- p3)(1-p1*p2)
= (1-0.65)(1 - 0.7 *0.75)
= 0.16625

b) X - system worked
A - S3 worked
B - S1 and S2 worked together
P(A|X) = P(A and X) /P(X) = P(A)/P(X)
= 0.65 / (1- 0.16625)
= 0.7796101

c) P(B|X) = P(B and X) /P(X)
= P(B) /P(X) = p1*p2 /(1- 0.16625)
= 0.7 *0.75 /(1- 0.16625)
=0.6296851

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