From the word `$POSSESSIVE$', a letter is chosen at random. The probability of it to be $S$ is

A box contains $10$ good articles and $6$ with defects. One article is chosen at random. What is the probability that it is either good or has a defect

For three non impossible events $A$, $B$ and $C$ $P\left( {A \cap B \cap C} \right) = 0,P\left( {A \cup B \cup C} \right) = \frac{3}{4},$ $P\left( {A \cap B} \right) = \frac{1}{3}$ and $P\left( C \right) = \frac{1}{6}$.

The probability, exactly one of $A$ or $B$ occurs but $C$ doesn't occur is 

A card is drawn at random from a well shuffled pack of $52$ cards. The probability of getting a two of heart or diamond is

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 :  $A^{\prime}$, $B^{\prime}, C$ are mutually exclusive and exhaustive.

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