# Q. 15.     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) =$\inline 0.2$                P(B fails alone) = $\inline 0.15$                P(A and B fail) = $\inline 0.15$                Evaluate the following probabilities                (i) $\inline P(A \; fails\mid B\; has\; failed)$

Answers (1)
S seema garhwal

Let event in which A fails and B fails be $E_A,E_B$

$P(E_A)=0.2$

$P(E_A\, and \, E_B)=0.15$

$P(B\, fails\, alone)=P(E_B)-P(E_A\, and\, E_B)$

$\Rightarrow \, \, \, 0.15=P(E_B)-0.15$

$\Rightarrow \, \, \, P(E_B)=0.3$

$P(E_A|E_B)=\frac{P(E_A\cap E_B)}{P(E_B)}$

$=\frac{0.15}{0.3}=0.5$

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