An electric component manufactured by a company is tested for its defectiveness by a sophisticated device. Let 'A' denote the event " the device is defective " and 'B' the event "t

Question

An electric component manufactured by a company is tested for its defectiveness by a sophisticated device. Let 'A' denote the event " the device is defective " and 'B' the event "the testing device reveals the component to be defective". Suppose $P (A) = α$ and $P (B / A) = P (\overset{ˉ}{B} / \overset{ˉ}{A}) = 1 - α$ . Where $0 < α < 1$ . If it is given that the testing device revels it to be defective , then the probability that the component is not defective is

Options:

Answer:

D

Solution:

$P (\frac{A ˉ}{B}) = \frac{P ( A ˉ ) \cdot P ( B / A ˉ )}{P ( A ) \cdot P ( B / A ) + P ( A ˉ ) \cdot P ( B / A ˉ )}$ $= \frac{( 1 - α ) α}{α ( 1 - α ) + ( 1 - α ) α} = \frac{1}{2}$

TestHub · Accepted Answer

P ( B A ˉ ​ ) = P ( A ) ⋅ P ( B / A ) + P ( A ˉ ) ⋅ P ( B / A ˉ ) P ( A ˉ ) ⋅ P ( B / A ˉ ) ​ = α ( 1 − α ) + ( 1 − α ) α ( 1 − α ) α ​ = 2 1 ​

Mathematics - Probability Question with Solution | TestHub

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