If the events $A$ and $B$ are mutually exclusive,then $P\left( \frac{A}{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?

If a die is rolled twice and the sum of the numbers appearing on them is observed to be $6$, then the probability that the number $1$ appears at least once on them is

Two events $A$ and $B$ are given. If $P(A) = \frac{1}{4}$,$P(A|B) = \frac{1}{2}$,and $P(B|A) = \frac{2}{3}$,then what is the value of $P(B)$?

Ten cards numbered $1$ to $10$ are placed in a box,mixed up thoroughly and then one card is drawn randomly. If it is known that the number on the drawn card is more than $3,$ what is the probability that it is an even number (in $/7$)?

If $A$ and $B$ are mutually exclusive events with $P(B) \neq 1$, then $P(A \mid \bar{B})$ is equal to (Here $\bar{B}$ is the complement of the event $B$)