An electronic assembly consists of two subsystems, say, A and B. From previous testing procedures, the following probabilities are assumed to be known:

P (A fails) = 0.2


P (B fails alone) = 0.15


P (A and B fail) = 0.15


Evaluate the following probabilities:


(i) P (A fails | B has failed)


(ii) P (A fails alone)

(i) Let us assume the event which is failed by A is denoted by EA

And, event which is failed by B is denoted by EB


It is given in the question that,


Event failed by A, P (EA) = 0.2


Event failed by both,


And, event failed by B alone


0.15 = P (EB) – 0.15


∴ P (EB) = 0.30


Hence,



= 0.5


(ii) We have,


Probability where A fails alone




15