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 $P(A$ fails alone$).$

Answer

Let us define events;
$A : A$ fails. and $B : B$ fails.
Given: $P (A) = 0.2$

Event failed by both, $P\left(A \cap B\right) = 0.15$
We have,
$P(A$ fails alone$) = P(A) -  P\left(A \cap B\right)$
$= 0.2 - 0.15$
$= 0.05$

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