Question

Assertion :For two events A & B such that $P\left(A\right)=P\left(A/B\right)=\frac{1}{4}$ & $P\left(B/A\right)=\frac{1}{2}$ then $P\left(\overline{A}/B\right)=\frac{3}{4}$ & $P\left(\overline{B}/A\right)=\frac{1}{2}$. Reason: Two events A & B are independent then $P\left(B/A\right)=P\left(B\right)$.

• 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

Since $P\left(A\right)=P\left(A/B\right)=\frac{1}{4}$

$\Rightarrow$ events $A$ & $B$ are independent

$\therefore P\left(B\right)=\frac{1}{2}=P\left(B/A\right)$

Now $P\left(A/B\right)=\frac{1}{4}and=P\left(B/A\right)=\frac{1}{2}$

$\therefore P\left(\overline{A}/B\right)=1-P\left(A/B\right)=1-\frac{1}{4}=\frac{3}{4}$

& $P\left(\overline{B}/A\right)=1-P\left(B/A\right)=1-\frac{1}{2}=\frac{1}{2}$