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 $P(A^{\prime} | B)$ is

$A$ and $B$ are mutually exclusive events of a random experiment and $P(B) \neq 1$,then $P(A \mid B^c) =$

An experiment has $10$ equally likely outcomes. Let $A$ and $B$ be two non-empty events of the experiment. If $A$ consists of $4$ outcomes,the number of outcomes that $B$ must have so that $A$ and $B$ are independent,is

If $E_{1}$ denotes the event of getting a sum of $6$ when throwing two dice and $E_{2}$ is the event of getting a $2$ on at least one of the two dice,then $P(E_{2} / E_{1})$ is (in $/ 5$)

$A$ family has two children. What is the probability that both the children are boys given that at least one of them is a boy?

$A$ and $B$ are independent events of a random experiment if and only if