Let $\quad S =\left\{ M =\left[ a _{ ij }\right], a _{ ij } \in\{0,1,2\}, 1 \leq i , j \leq 2\right\}$ be a sample space and $A=\{M \in S: M$ is invertible $\}$ be an event. Then $P ( A )$ is equal to

Let $M$ be the maximum value of the product of two positive integers when their sum is $66$. Let the sample space $S=\left\{x \in Z: x(66-x) \geq \frac{5}{9} M\right\}$ and the event $A=\{ x \in S : x$ is a multiple of $3$ $\}$. Then $P ( A )$ is equal to

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?

Five horses are in a race. $Mr. \,A$ selects two of the horses at random and bets on them. The probability that $Mr.\, A$ selected the winning horse is

A die is thrown. Describe the following events : $A$ : a number less than $7.$ , $B:$ a number greater than $7.$ Find the $A \cap B$