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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 =0.15P(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 EA and EB.
P(EA)=0.2
P(EAEB)=0.15
P(B fails alone)=P(EB)P(EAEB)
0.15=P(EB)0.15
P(EB)=0.3
(i) P(EA U EB)=P(EA)+P(EB)P(EAEB)
0.2+0.30.15=0.35
(ii) P(A fails alone)=P(EA)P(EAEB)
=0.20.15
=0.05

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