Two dice are thrown simultaneously. What is the probability of obtaining a multiple of $2$ on one of them and a multiple of $3$ on the other?

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

$A$ fair die is rolled once. Let $A$ be the event of getting an integer greater than $3$ and $B$ be the event of getting an integer less than $5$. Find $P(A \cup B)$.

The probability that a number selected at random from the set of numbers $(1, 2, 3, \ldots, 100)$ is a cube,is

$A$ problem in Algebra is given to two students $A$ and $B$ whose chances of solving it are $\frac{2}{5}$ and $\frac{3}{4}$ respectively. The probability that the problem is solved, if both of them try independently, is

Let $N$ denote the sum of the numbers obtained when two dice are rolled. If the probability that $2^{N} < N!$ is $\frac{m}{n}$,where $m$ and $n$ are coprime,then $4m - 3n$ is equal to $......$.