Question

On throwing a fair die, the probabilities of rolling greater than $2$ but less than $3$ is .

Answer 1

For rolling a fair die,
$\text{Sample Space}=\{1,2,3,4,5,6\}$
$\therefore$ Total number of possible 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
$\text{P (2<number<3)}=\frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}$

$\Rightarrow \text{P(2<number<3)}=\frac{0}{6}=0$

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