If $A$ and $B$ are two events such that $P(A) = \frac{1}{3}$,$P(B) = \frac{1}{4}$ and $P(A \cap B) = \frac{1}{5}$,then $P\left( \frac{\overline{B}}{\overline{A}} \right) = $

$A$ bag contains $4$ Red and $6$ Black balls. $A$ ball is drawn at random from the bag,its colour is observed and this ball along with $3$ additional balls of the same colour are returned to the bag. If now a ball is drawn at random from the bag,then the probability that this drawn ball is red is

In a city,$40\%$ of the people have brown hair,$25\%$ have brown eyes,and $15\%$ have both brown hair and brown eyes. If a person is selected at random from those having brown hair,what is the probability that they also have brown eyes?

$A$ and $B$ are two events such that $P(A) \neq 0$. Find $P(B \mid A)$ if: $(i)$ $A \subset B$ (ii) $A \cap B = \phi$.

$A$ couple has two children. One of them is a boy. What is the probability that the other child is also a boy?

If $A$ and $B$ are two events such that $P(\bar{A})=0.3, P(B)=0.4$ and $P(A \cap \bar{B})=0.5$, then $P(B \mid A \cup \bar{B})=$