$A$ single letter is selected at random from the word $PROBABILITY$. The probability that the selected letter is a vowel is

If a number $x$ is drawn randomly from the set of numbers $\{1, 2, 3, \ldots, 50\}$,then the probability that the number $x$ satisfies the inequation $x + \frac{10}{x} \leq 11$ is

The probability that a non-leap year contains $53$ Sundays is

In a random experiment of selecting a ticket from $50$ tickets numbered $00, 01, 02, 03, ..., 47, 49$,if a ticket is selected such that the product of its digits is $0$,what is the probability that the sum of its digits is $8$?

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?

If the events $A$ and $B$ are mutually exclusive events such that $P(A) = \frac{3x + 1}{3}$ and $P(B) = \frac{1 - x}{4}$,then the set of possible values of $x$ lies in the interval