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 $P\left(\frac{B}{A}\right)$.

If $A$ and $B$ are two events such that $A \subset B$ and $P(B) \neq 0$,then which of the following is correct?

Suppose $E$ and $F$ are two events of a random experiment. If the probability of occurrence of $E$ is $1/5$ and the probability of occurrence of $F$ given $E$ is $1/10$, then the probability of non-occurrence of at least one of the events $E$ and $F$ is

If $A$ and $B$ are events,such that $P(A) = \frac{1}{4}$,$P(A|B) = \frac{1}{2}$,and $P(B|A) = \frac{2}{3}$,then $P(B)$ is

Find $P(E | F)$ for a coin tossed three times,where $E$ is the event 'at least two heads' and $F$ is the event 'at most two heads'.

If $A$ and $B$ are two events such that $P(A) \neq 0$ and $P(B \mid A) = 1$,then . . . . . . .