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

If $A$ and $B$ are two independent events such that $P(A \cap B') = \frac{3}{25}$ and $P(A' \cap B) = \frac{8}{25}$,then $P(A) = $

Statement $- I :$ If $A$ and $B$ are two independent events such that $P(A) = 1/2$ and $P(B) = 1/5$,then $P(A|B) = 1/2$.
Statement $- II : P(A|B) = P(A)$ if $A$ and $B$ are independent events.

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 $B$)

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'.

Let $A$ and $B$ be two events such that $P(A) = \frac{3}{8}$, $P(B) = \frac{5}{8}$ and $P(A \cup B) = \frac{3}{4}$. Then $P(A'|B) - P(A|B) =$ . . . . . .