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 the events $A$ and $B$ are mutually exclusive,then $P\left( \frac{A}{B} \right) = $

In a random experiment,events $A$ and $B$ are such that $P(A) = \frac{1}{4}$,$P(A \mid B) = \frac{1}{2}$,and $P(B \mid A) = \frac{2}{3}$. Find $P(B)$.

$A$ and $B$ are two groups of books. Group $A$ consists of $8$ science and $5$ engineering books,and group $B$ consists of $6$ science and $7$ engineering books. When an unbiased die is rolled,if $2$ or $5$ turns up,a book is selected at random from group $A$. Otherwise,a book is selected at random from group $B$. The probability of selecting a science book is

Let $A$ and $B$ be two events such that $P(A) = \frac{5}{11}$,$P(B) = \frac{2}{11}$,and $P(A \cup B) = \frac{3}{11}$,then $P(A'|B')$ 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 $P(B)$?