$A$ 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 $P(A \cup B)$.

An integer $x$ is chosen from $1$ to $50.$ Then the probability that $x + \frac{336}{x} \le 50$ is

The probabilities of two persons to hit a target are $\frac{1}{4}$ and $\frac{1}{5}$ respectively. The probability that the target is being hit when both of them attempt independently is

An experiment involves rolling a pair of dice and recording the numbers that come up. Describe the following events:
$A:$ the sum is greater than $8$.
$B:$ $2$ occurs on either die.
$C:$ the sum is at least $7$ and a multiple of $3$.
Which pairs of these events are mutually exclusive?

In a single throw of two dice,what is the probability of getting a total of $13$?

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