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 $8$?

The probability that a randomly selected $2$-digit number belongs to the set $\{n \in N : (2^{n}-2) \text{ is a multiple of } 3\}$ is equal to:

Three groups of children $A$, $B$, and $C$ contain boys and girls as given below. Group $A$ contains $3$ girls and $1$ boy, group $B$ contains $2$ girls and $2$ boys, and group $C$ contains $3$ boys and $1$ girl. If $1$ child is selected at random from each group, what is the probability that the three children selected consist of $1$ girl and $2$ boys?

Given $f(x) = x^2 - 5x + 4$. If a number $x$ is chosen at random from the first $20$ natural numbers,then the probability that the chosen $x$ satisfies the inequality $f(x) > 10$ is

For two events $A$ and $B$,if $P(A \cup B) = \frac{5}{6}$,$P(A) = \frac{1}{6}$,and $P(B) = \frac{2}{3}$,then $A$ and $B$ are:

$A$ die is thrown. Find the probability of the following event: $A$ number more than $6$ will appear.