$A$ fair die is rolled once. Let $A$ be the event of getting an integer greater than $3$ and $B$ be the event of getting an integer less than $5$. Find $P(A \cup B)$.

$A$ coin is tossed. If the outcome is a head,a die is thrown. If the die shows up an even number,the die is thrown again. What is the sample space for the experiment?

Three coins are tossed. Describe three events which are mutually exclusive but not exhaustive.

$A$ box contains $100$ tickets numbered $1$ to $100$. $A$ ticket is drawn at random from the box. Then the probability that the number on the ticket is a perfect square is

Let $A$ and $B$ be two events such that $P(\overline{A \cup B}) = \frac{1}{6}$,$P(A \cap B) = \frac{1}{4}$,and $P(\bar{A}) = \frac{1}{4}$,where $\bar{A}$ stands for the complement of event $A$. Then events $A$ and $B$ are

$A$ lot consists of $12$ good pencils,$6$ with minor defects,and $2$ with major defects. $A$ pencil is chosen at random. The probability that this pencil is not defective is