Let two fair dice $A$ and $B$ be thrown. What is the probability that the number appearing on dice $A$ is greater than the number appearing on dice $B$?

$2$ boys and $2$ girls are in Room $X$,and $1$ boy and $3$ girls are in Room $Y$. Specify the sample space for the experiment in which a room is selected and then a person.

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

$A$ and $B$ are two events such that $P(A)=0.58$,$P(B)=0.32$ and $P(A \cap B)=0.28$. Then the probability that neither $A$ nor $B$ occurs 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?

$A$ bag contains $5$ black balls, $4$ white balls and $3$ red balls. If a ball is selected at random, the probability that it is a black or a red ball, is