4) There is 0.01 probability that an electrical connector that is kept dry fails

Question

4) There is 0.01 probability that an electrical connector that is kept dry fails during the warranty period. If the connector is ever wet, the probability of a failure during the warranty period is 0.05. Generally, 0.9 of the connectors are kept dry and 0.1 are wet a) What the probability of a connector failure during the warranty period? b) Given that a failure is reported, what is the probability of connector ever got wet? c) Are connector failure and connector getting wet during warranty period independent? (You can answer part c based on your part b solution)

Explanation / Answer

Let A be the event of failure of the electrical connector

B be the event that electrical connector is dry and C be the event that electrical connector is wet

P(B) = 0.9 and p(C) = 0.1

P(A given B) = 0.01 and P(A given CV) = 0.05

(a) P(A) = 0.9*0.01+0.1*0.05 = 0.014

(b) P(C given A) = P(A given C)/P(A) = (0.05*0.1)/0.014 = 0.3571

(c) P(C given A) = (P(C)*P(A))/P(A) = (0.1*0.05)/0.014 = 0.3571

Yes C and A are independent as P(A intersection C) = P(A)*P(C)

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