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 $B$ ) failing $= 0.15$
Evaluate the following probabilities:
(i) $P$ ( $A$ fails or $B$ fails)
(ii) $P$ ( $A$ fails alone)

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Solution

Let the event in which $A$ fails and $B$ fails be denoted by $E_{A}$ and $E_{B}$ .
$P (E_{A}) = 0.2$
$P (E_{A} \cap E_{B}) = 0.15$
$P (B f a i l s a l o n e) = P (E_{B}) - P (E_{A} \cap E_{B})$
$\Rightarrow 0.15 = P (E_{B}) - 0.15$
$\Rightarrow P (E_{B}) = 0.3$
(i) $P (E_{A} U E_{B}) = P (E_{A}) + P (E_{B}) - P (E_{A} \cap E_{B})$
$0.2 + 0.3 - 0.15 = 0.35$
(ii) $P (A f a i l s a l o n e) = P (E_{A}) - P (E_{A} \cap E_{B})$
$= 0.2 - 0.15$
$= 0.05$

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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 =0.2P(B) fails alone =0.15P(A and B) failing =0.15Evaluate the following probabilities:(i) P(A fails or B fails) (ii) P (A fails alone)

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