Question

On throwing a fair die, the probabilities of rolling greater than $2$ but less than $3$ and greater than $0$ areand, respectively.

• A. $\frac{1}{6}$
• B. $\frac{1}{2}$
• C. $1$
• D. $0$
• E. $\frac{1}{3}$

Answer 1

Answer: (C), (D)

$0$

For rolling a fair die,
$\text{Sample Space}=\{1,2,3,4,5,6\}$
$\therefore$ Total number of equally likely outcomes= $6$

$\bullet$ For rolling greater than $2$ but less than $3$, the number of favorable outcomes is $0$ as there is no number in the sample space which is greater than $2$ but less than $3$.

Hence, the probability of rolling greater than $2$ but less than $3$ is
$\text{P (2<number<3)}=\frac{\text{Number of favorable outcomes}}{\text{Total number of equally likely outcomes}}$
$\Rightarrow \text{P(2<number<3)}=\frac{0}{6}=0$

$\therefore$ As the probability of rolling greater than $2$ but less than $3$ is $0$, it is an $\text{impossible event}$.

$\bullet$ For rolling greater than $0$,
Favorable outcomes= $\{1,2,3,4,5,6\}$
(As all the numbers in the sample space are greater than $0$)
$\therefore$ Number of favorable outcomes= $6$

Hence, the probability of rolling greater than $0$ is
$\text{P (number>0)}=\frac{\text{Number of favorable outcomes}}{\text{Total number of equally likely outcomes}}$
$\Rightarrow \text{P (number>0)}=\frac{6}{6}=1$

$\therefore$ As the probability of rolling greater than $0$ is $1$, it is a $\text{certain event}$.