Given $P(A)=0.5, P(B)=0.4, P(A \cap B)=0.3$,then $P(A^{\prime} / B^{\prime})$ is equal to

If $P(A)=0.8, P(B)=0.5$ and $P(B | A)=0.4,$ find $P(A | B).$

$A$ 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 $P(A) = \frac{3}{8}$, $P(B) = \frac{5}{8}$ and $P(A \cup B) = \frac{3}{4}$. Then $P(A'|B) - P(A|B) =$ . . . . . .

Two integers are selected at random from the set $\{1, 2, \dots, 11\}.$ Given that the sum of the selected numbers is even,what is the conditional probability that both numbers are even?

If $A$ and $B$ are two events of a sample space $S$ such that $P(A)=0.2$,$P(B)=0.6$ and $P(A \mid B)=0.5$,then $P(A^{\prime} \mid B) = $