Two integers $r$ and $s$ are drawn one at a time without replacement from the set $\{1, 2, \ldots, n\}$. Then $P(r \leq k \mid s \leq k) =$

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) = $

Consider the following statements.
Statement $(I)$: If $E$ and $F$ are two independent events,then $E^{\prime}$ and $F^{\prime}$ are also independent.
Statement $(II)$: Two mutually exclusive events with non-zero probabilities of occurrence cannot be independent.
Which of the following is correct?

If $C$ and $D$ are two events such that $P(D) \neq 0$,then which of the following statements is correct?

If $P(A / B) = \frac{3}{10}$, $P(B / A) = \frac{4}{5}$ and $P(A \cup B) = K P(B)$, then $\frac{1}{K} =$

Two dice are rolled. If $A$ denotes the event that the same number shows on each die and $B$ denotes the event that the sum of the numbers on both dice is greater than $7$,then $P(A \mid B)$ and $P(B \mid A)$ respectively are