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 fails)=0.15

Evaluate the following probabilities

P(A fails alone)

Answer 1

Let the event in which A fails and B fails be denoted by A' and B'

P(A')=0.2, $P(A^{\prime }\cap B^{\prime })=0.15$

P(B fails alone)= P(B')- $P(A^{\prime }\cap B^{\prime })$

$\therefore$ 0.15= P(B')-0.15

$\Rightarrow$ P(B')=0.30

P(A fails alone) =P(A fails) -P(Both A and B fails)

=$P\left(A^{\prime }\right)-P(A^{\prime }\cap B^{\prime })=0.2-0.15=0.05$