Question

The probability of not rolling 8 with a single six-sided fair die is .

Answer 1

For rolling a six-sided fair die, the sample space is $\{1,2,3,4,5,6\}$, i.e., the total number of outcomes is $6$.

For the event of rolling $8$, the number of favorable outcomes is $0$ as there is no $8$ in the sample space.

$\therefore \text{P(rolling}8\text{)}=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$

$\Rightarrow \text{P(rolling}8\text{)}=\frac{0}{6}=0$

We know,
$\text{P(not rolling}8\text{)}=1-\text{P(rolling}8\text{)}$
$\Rightarrow \text{P(not rolling}8\text{)}=1-0$
$\Rightarrow \text{P(not rolling}8\text{)}=1$

$\therefore$ The probability of NOT rolling $8$ is $1$. Hence, the event of NOT rolling $8$ with a six-sided fair die is a certain event.