$A$ die is thrown. Find the probability of the following event: $A$ number greater than or equal to $3$ will appear.

Describe the sample space for the indicated experiment: $A$ coin is tossed three times.

An experiment consists of recording the boy-girl composition of families with $2$ children. What is the sample space if we are interested in knowing whether it is a boy or girl in the order of their births?

$A$ 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 $\frac{1}{5}$. If they appear for the interview independently,then the probability that only one of them is selected is:

If $x$ is chosen at random from the set $\{1, 2, 3, 4\}$ and $y$ is chosen at random from the set $\{5, 6, 7\}$,then the probability that $xy$ will be even is

If $A$ and $B$ are any two events such that $P(\overline{A \cup B}) = \frac{1}{6}$,$P(A \cap B) = \frac{1}{4}$,and $P(\bar{A}) = \frac{1}{4}$,then the events $A$ and $B$ are