NCERT Class XII Mathematics Chapter - - Solutions
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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)
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 A and B
Thus, P(A fails)= P ( A ) = 0 2.
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 ) =
=
= 0.5
(ii) P(A fails alone)= P ( A ) − P ( A ∩ B ) = 0.2 − 0.15 = 0.05
Thus, P(A fails)
P (A and B fails)
P (B fails alone)
(i) P (A fails|B has failed)
(ii) P(A fails alone)
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