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 $P(\text{not } A \text{ and not } B)$.

$A$ man and his wife appear for an interview for two posts. The probability of the husband's selection is $\frac{1}{7}$ and that of the wife's selection is $\frac{1}{5}$. What is the probability that only one of them will be selected?

Two integers $x$ and $y$ are chosen with replacement from the set $\{0, 1, 2, 3, \ldots, 10\}$. Then the probability that $|x-y| > 5$ is:

If a dice is thrown twice,then the probability of getting $1$ in the first throw only is

There are $3$ families,each having $1$ boy and $1$ girl. If one child is selected from each family,what are the elements of the event that only girls are selected?

From $10,000$ lottery tickets numbered from $1$ to $10,000$,one ticket is drawn at random. What is the probability that the number marked on the drawn ticket is divisible by $20$?