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

a) here probability of a connector failure during warranty period =P(failure) =P(dry and failed+wet and failed)

=0.9*0.01+0.1*0.05=0.014

b) probability of connector got wet given failure P(wet|failure)=P(wet and failed)/P(failure )=0.1*0.05/0.014=0.3571

c) no as P(wet|failure) is not equal to probability of getting wet whcih is equal to 0.1 ; therefore not independent.

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