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 fails) = 0.15 Evaluate the following probabilities (i) P(A fails|B has failed) (ii) P(A fails alone)

NCERT Class XII Mathematics Chapter - - Solutions

Question : 97

Total: 101

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 fails) = 0.15
Evaluate the following probabilities
(i) P(A fails|B has failed)
(ii) P(A fails alone)

Solution:

Let A‌and‌B denote the events A fails and B fails respectively
Thus, P(A fails) =P(A)=02.
P (A and B fails) =P(A∩B)=0.15
P (B fails alone) =P(B)−P(A∩B)=0.15
⇒P(B)−0.15=0.15
⇒P(B)=0.30
(i) P (A fails|B has failed)
P(A|B)=

P(A∩B)

P(B)

0.15

0.30

=0.5
(ii) P(A fails alone) =P(A)−P(A∩B) =0.2−0.15=0.05

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