Let A and B be two independent events such that

Question:

Let $A$ and $B$ be two independent events such that $P(A)=\frac{1}{3}$ and $P(B)=\frac{1}{6}$. Then, which of the following is TRUE ?

  1. (1) $P(A / B)=\frac{2}{3}$

  2. (2) $P\left(A / B^{\prime}\right)=\frac{1}{3}$

  3. (3) $P\left(A^{\prime} / B^{\prime}\right)=\frac{1}{3}$

  4. (4) $P(A /(A \cup B))=\frac{1}{4}$

Correct Option: , 2

Solution:

$\mathrm{A}$ and $\mathrm{B}$ are independent events.

So, $P\left(\frac{A}{B^{\prime}}\right)=\frac{P\left(A \cap B^{\prime}\right)}{P\left(B^{\prime}\right)}=\frac{\frac{1}{3}-\frac{1}{3} \cdot \frac{1}{6}}{\frac{1}{6}}=\frac{1}{3}$

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