Let $S$ be a set containing $n$ elements. If we select $2$ subsets $A$ and $B$ of $S$ at random,then the probability that $A \cup B = S$ and $A \cap B = \phi$ is:

In the random experiment of tossing two unbiased dice, let $E$ be the event of getting the sum $8$ and $F$ be the event of getting even numbers on both the dice. Then:
$I. P(E) = \frac{7}{36}$
$II. P(F) = \frac{1}{3}$
Which of the following is a correct statement?

$A$ coin and a six-faced die,both unbiased,are thrown simultaneously. The probability of getting a head on the coin and an odd number on the die is:

An experiment consists of recording the boy-girl composition of families with $2$ children. What is the sample space if we are interested in knowing whether it is a boy or girl in the order of their births?

Let $S_n = \sum_{k=1}^n k$ denote the sum of the first $n$ positive integers. The numbers $S_1, S_2, S_3, \ldots, S_{99}$ are written on $99$ cards. The probability of drawing a card with an even number written on it 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: $A', B', C$ are mutually exclusive and exhaustive.