A die has two faces each with number $^{\prime}1^{\prime}$ , three faces each with number $^{\prime}2^{\prime}$ and one face with number $^{\prime}3^{\prime}$. If die is rolled once, determine $P (2)$.

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 ..... .

A bag contains $19$ tickets numbered from $1$ to $19$. A ticket is drawn and then another ticket is drawn without replacement. The probability that both the tickets will show even number, is

Find the sample space associated with the experiment of rolling a pair of dice (one is blue and the other red) once. Also, find the number of elements of this sample space.

Let $E _{1}, E _{2}, E _{3}$ be three mutually exclusive events such that $P \left( E _{1}\right)=\frac{2+3 p }{6}, P \left( E _{2}\right)=\frac{2- p }{8}$ and $P \left( E _{3}\right)$ $=\frac{1- p }{2}$. If the maximum and minimum values of $p$ are $p _{1}$ and $p _{2}$, then $\left( p _{1}+ p _{2}\right)$ is equal to.

A coin is tossed $3$ times by $2$ persons. What is the probability that both get equal number of heads