Let $A$ be a set of all $4 -$digit natural numbers whose exactly one digit is $7 .$ Then the probability that a randomly chosen element of  $A$ leaves remainder $2$ when divided by $5$ is ..... .

On her vacations Veena visits four cities $(A,\,B ,\, C$ and $D$ ) in a random order. What is the probability that she visits $A$ before $B$ ?

Let $\mathrm{X}$ and $\mathrm{Y}$ be two events such that $\mathrm{P}(\mathrm{X})=\frac{1}{3}, \mathrm{P}(\mathrm{X} \mid \mathrm{Y})=\frac{1}{2}$ and $\mathrm{P}(\mathrm{Y} \mid \mathrm{X})=\frac{2}{5}$. Then

$[A]$ $\mathrm{P}\left(\mathrm{X}^{\prime} \mid \mathrm{Y}\right)=\frac{1}{2}$   $[B]$ $\mathrm{P}(\mathrm{X} \cap \mathrm{Y})=\frac{1}{5}$    $[C]$ $\mathrm{P}(\mathrm{X} \cup \mathrm{Y})=\frac{2}{5}$    $[D]$ $\mathrm{P}(\mathrm{Y})=\frac{4}{15}$

A letter is chosen at random from the word $\mathrm {'ASSASSINATION'}$. Find the probability that letter is a vowel.

There are two childrens in a family. The probability that both of them are boys is

The probability of getting number $5$ in throwing a dice is