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

If $A$ and $B$ are two events such that $P(A) \neq 0$ and $P(B) \neq 1$,then $P\left( \frac{\overline{A}}{\overline{B}} \right) = $

Let $A$ and $B$ be independent events with $P(B) = \frac{2}{5}$ and $P(A \cup B) = \frac{11}{20}$. Then $P(A' \mid B)$ is a root of which equation?

$A$ fair die is tossed until a six is obtained. Let $X$ be the number of required tosses,then the conditional probability $P(X \geq 5 \mid X > 2)$ is:

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

Let $A$ and $B$ be not mutually exclusive events. If $P(A) = \frac{4}{9}$ and $P(A \cap \bar{B}) = \frac{3}{7}$, then find $P\left(\frac{B}{A}\right)$.