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 E_A

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

It is given in the question that,

Event failed by A, P (E_A) = 0.2

Event failed by both,

And, event failed by B alone

0.15 = P (E_B) – 0.15

∴ P (E_B) = 0.30

Hence,

= 0.5

(ii) We have,

Probability where A fails alone