$A$ die is thrown. Find the probability of the following event: $A$ number less than or equal to $1$ will appear.

If $A$ and $B$ are two events such that $P(A) = \frac{1}{4}$,$P(B) = \frac{1}{2}$,and $P(A \cap B) = \frac{1}{8}$,find $P(\text{not } A \text{ and not } B)$.

Two fair dice are rolled. The probability of the sum of digits on their faces being greater than or equal to $10$ is

The probability of obtaining an even prime number on each die,when a pair of dice is rolled,is . . . . . . .

If two subsets $A$ and $B$ are selected at random from a set $S$ containing $n$ elements,then the probability that $A \cap B = \phi$ and $A \cup B = S$ is

$P, Q$ and $R$ try to hit the same target one after the other. If their probabilities of hitting the target are $\frac{2}{3}, \frac{3}{5}, \frac{5}{7}$ respectively,then the probability that the target is hit by $P$ or $Q$ but not by $R$ is