Question

Match the followings if a fair die is rolled once. Here, P stands for the probability.

• A. $0$
• B. $\frac{1}{2}$
• C. $1$

Answer 1

A fair die is rolled once.

Possible outcomes= $\{1,2,3,4,5,6\}$
$\therefore$ Number of possible outcomes= $6$

Outcomes with prime numbers= $\{2,3,5\}$
$\therefore$ Number of outcomes with prime numbers= $3$

$\text{P (Prime number)}=\frac{\text{Number of outcomes with prime numbers}}{\text{Total possible outcomes}}$
$\Rightarrow \underset{–}{\text{P (Prime number)}=\frac{3}{6}=\frac{1}{2}}$


Number of outcome with $‘‘0"$= $0$ ($\because$ there is no face in the die with $‘‘0"$)

$\text{P (0)}=\frac{\text{Number of outcome with}‘‘0"}{\text{Total possible outcomes}}$

$\Rightarrow \underset{–}{\text{P (0)}=\frac{0}{6}=0}$


Outcomes belong to natural numbers = $\{1,2,3,4,5,6\}$
$\therefore$ Number of outcomes belongs to natural numbers = $6$

$\text{P (Natural number)}=\frac{\text{Number of outcomes belong to natural numbers}}{\text{Total possible outcomes}}$
$\Rightarrow \underset{–}{\text{P (Natural number)}=\frac{6}{6}=1}$