Two dice are thrown and the sum of the numbers appeared on the dice is noted. If $A$ is the event of getting a prime number as their sum and $B$ is the event of getting a number greater than $8$ as their sum,then $P(A \cap \overline{B})=$

If $A, B,$ and $C$ can hit a target $4$ out of $5$ times,$3$ out of $4$ times,and $2$ out of $3$ times respectively,what is the probability that exactly two of them hit the target?

Let $S$ be the set of all quadratic equations of the form $x^2+bx+c=0$,where $b, c \in \{1, 2, 3, 4, 5, 6\}$. If an equation is selected at random from $S$,then the probability that the equation has real roots is

One card is drawn at random from a well-shuffled pack of $52$ cards. The probability that the card drawn is a face card (Jack,Queen,and King only) is

Thirty-two persons $X_1, X_2, \ldots, X_{32}$ are randomly seated around a circular table at equal intervals. Two persons $X_i$ and $X_j$ are said to be within earshot of each other if there are at most three persons between them on the minor arc joining $X_i$ and $X_j$. The probability that $X_1$ and $X_3$ are within earshot of each other is:

Two students Anil and Ashima appeared in an examination. The probability that Anil will qualify the examination is $0.05$ and that Ashima will qualify the examination is $0.10$. The probability that both will qualify the examination is $0.02$. Find the probability that both Anil and Ashima will not qualify the examination.