An electronic assembly consists of two subsystems, say, A and B. From previous testing procedures, the following probabilities are assumed to be known: $ \text {P(A fails) = 0.2 P(B fails alone) = 0.15 P(A and B fail) = 0.15}$. Evaluate the following probabilities \[ \text {(i) P(A fails | B has failed) (ii) P(A fails alone)} \]

Question

$\begin{array}{1 1}(i) 0.5 (ii) 0.05 \\ (i) 0.05 (ii) 0.05 \\(i) 0.05 (ii) 0.5 \\(i) 0.5 (ii) 0.5 \end{array} $