JEE MainMathematicsEasyProbability

An electric component manufactured by a company is tested for
its defectiveness by a sophisticated device. Let denote the event
"the device is defective" and B denote event "The testing device
reveals the component to be defective". Suppose
$P

Show answer and solution

P(\overset{¯}{A}/B) = \frac{P(\overset{¯}{A})P(B/\overset{¯}{A})}{P(A)P(B/A) + P(\overset{¯}{A})P(B/\overset{¯}{A})} = \frac{(1 - \alpha)\alpha}{\alpha(1 - \alpha) + (1 - \alpha)\alpha} = \frac{1}{2}

p = \frac{1}{2}

\Rightarrow 16p = 8

Source: Grass-G / M-28 Mathematics Paper FST 16 Jan.docx

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