Question

Assertion :If $P\left(A/B\right)>P\left(A\right)$ then. $P\left(B/A\right)>P\left(B\right)$. Reason: If events A & B are dependent, then $P\left(A/B\right)=\frac{P(A\cap B)}{P\left(B\right)}$.

• A. Both Assertion & Reason are individually true & Reason is correct explanation of Assertion
• B. Both Assertion & Reason are individually true but Reason is not the ,correct (proper) explanation of Assertion
• C. Assertion is true but Reason is false
• D. Assertion is false but Reason is true

Answer 1

The correct option is A Both Assertion & Reason are individually true & Reason is correct explanation of Assertion

$P\left(A/B\right)=\frac{P(A\cap B)}{P\left(B\right)}$.....( i )
Now $P\left(A/B\right)>P\left(A\right)$
$\Rightarrow \frac{P(A\cap B)}{P\left(B\right)}>P\left(A\right)\Rightarrow \frac{P(A\cap B)}{P\left(A\right)}>P\left(B\right)$
$\Rightarrow P\left(B/A\right)>P\left(B\right)$
Hence Assertion is followed by Reason.