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 $\leq 5$

Describe the events not $B$

An experiment consists of recording boy-girl composition of families with $2$ children. What is the sample space if we are interested in the number of girls in the family?

The probability of obtaining sum ‘$8$’ in a single throw of two dice

Two numbers are selected randomly from the set $S = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}$ without replacement one by one. The probability that minimum of the two numbers is divisible by $3$ or maximum of the two numbers is divisible by $4$ , is 

Let $A$ be a set of all $4 -$digit natural numbers whose exactly one digit is $7 .$ Then the probability that a randomly chosen element of  $A$ leaves remainder $2$ when divided by $5$ is ….. .