Search any question & find its solution
Question:
Answered & Verified by Expert
If $A$ and $B$ are two events such that $P(A)=\frac{1}{3}, P(B)=\frac{1}{2}$ and $P(A \cap B)=\frac{1}{6}$, then $P\left(A^{\prime} / B\right)$ is
Options:
Solution:
2653 Upvotes
Verified Answer
The correct answer is:
$\frac{2}{3}$
Given $P(A)=\frac{1}{3}, P(B)=\frac{1}{2}$ and $P(A \cap B)=\frac{1}{6}$
$\begin{aligned}
P\left(A^{\prime} / B\right) &=\frac{P\left(A^{\prime} \cap B\right)}{P(B)}=\frac{P(B)-P(A \cap B)}{P(B)} \\
&=\frac{\frac{1}{2}-\frac{1}{6}}{1 / 2}=\frac{2}{3}
\end{aligned}$
$\begin{aligned}
P\left(A^{\prime} / B\right) &=\frac{P\left(A^{\prime} \cap B\right)}{P(B)}=\frac{P(B)-P(A \cap B)}{P(B)} \\
&=\frac{\frac{1}{2}-\frac{1}{6}}{1 / 2}=\frac{2}{3}
\end{aligned}$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.