Q91 / 180 · KCET 2020 · Mathematics

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

  • Correct answer
    A
    $\frac{2}{3}$
  • B
    $\frac{1}{3}$
  • C
    $\frac{1}{2}$
  • D
    $\frac{1}{12}$

Solution

Given $P(A)=\frac{1}{3}, P(B)=\frac{1}{2}$ and $P(A \cap B)=\frac{1}{6}$ $\begin{aligned} P\left(A^{\prime} / B\right) &=\frac{P\left(A^{\prime} \cap B\right)}{P(B)}=\frac{P(B)-P(A \cap B)}{P(B)} \\ &=\frac{\frac{1}{2}-\frac{1}{6}}{1 / 2}=\frac{2}{3} \end{aligned}$

Hence, the correct answer is option: 'A'.

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