A determinant is chosen at random. The set of all determinants of order $2$ with elements $0$ or $1$ only. The probability that value of the determinant chosen is positive, is

Two dice are thrown. The probability that the sum of the points on two dice will be $7$, is

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?

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 $C$ are mutually exclusive

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

Three coins are tossed. Describe Two events, which are not mutually exclusive.