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

A die is rolled. Let $E$ be the event "die shows $4$ " and $F$ be the event "die shows even number". Are $E$ and $F$ mutually exclusive ?

The probability that a leap year selected randomly will have $53$ Sundays is

Three coins are tossed once. Find the probability of getting at most $2$ heads.

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 $B$ are mutually exclusive

From $10,000$ lottery tickets numbered from $1$ to $10,000$, one ticket is drawn at random. What is the probability that the number marked on the drawn ticket is divisible by $20$