Consider the experiment of rolling a die. Let $A$ be the event 'getting a prime number ', $B$ be the event 'getting an odd number '. Write the sets representing the events $A$ and $B$

Suppose $3$ bulbs are selected at random from a lot. Each bulb is tested and classified as defective $(D)$ or non-defective $(N)$. Write the sample space of this experiment?

Find the sample space associated with the experiment of rolling a pair of dice (one is blue and the other red) once. Also, find the number of elements of this sample space.

There are four men and six women on the city council. If one council member is selected for a committee at random, how likely is it that it is a woman?

A die is thrown, find the probability of following events: A number more than $6$ will appear,

Two dice are thrown. The events $A,\, B$ and $C$ are as follows:

$A:$ getting an even number on the first die.

$B:$ getting an odd number on the first die.

$C:$ getting the sum of the numbers on the dice $\leq 5$

State true or false $:$ (give reason for your answer)

Statement : $A$ and $B^{\prime }$ are mutually exclusive