Let $X$ be a set containing $n$ elements. If two subsets $A$ and $B$ of $X$ are picked at random,the probability that $A$ and $B$ have the same number of elements is:

$A$ bag consists of $3$ red balls,$5$ blue balls and $8$ green balls. $A$ ball is selected at random. What is the probability of not getting a blue ball?

Three coins are tossed. Describe two events which are mutually exclusive but not exhaustive.

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.

One card is drawn from a well-shuffled deck of $52$ cards. If each outcome is equally likely,calculate the probability that the card will be a black card (i.e.,a club or a spade).

The probabilities of a student getting $I, II$ and $III$ division in an examination are respectively $\frac{1}{10}, \frac{3}{5}$ and $\frac{1}{4}$. The probability that the student fails in the examination is