Question

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)

Answer 1

Let the event in which A fails and B fails be denoted by E_A and E_B.

P (E_A) = 0.2 

P (E_A and E_B) = 0.15 

P (B fails alone) = P (E_B) − P (E_A and E_B) 

∴ 0.15 = P (E_B) − 0.15

 ∴ P (E_B) = 0.3

(ii) P (A fails alone) = P (E_A) − P (E_{A and} E_B)

 = 0.2 − 0.15

 = 0.05