Question

A fair die is thrown. What is the probability of not rolling a factor of $5?$

• A. $\frac{2}{3}$
• B. $\frac{1}{3}$
• C. $\frac{5}{6}$
• D. $\frac{1}{6}$

Answer 1

The correct option is A $\frac{2}{3}$

On rolling a fair die, the number of possible outcomes is $6$.

The numbers on the die that are factors of $5$ are $1,\text{and}5.$

$\therefore$ On rolling a factor of $5$, the number of favorable outcomes is $2$.

Now,
$\text{P(rolling a factor of 5)}=\frac{\text{Number of numbers on die which are factor of 5}}{\text{Total number of numbers on die}}$

$\Rightarrow \text{P(rolling a factor of 5)}=\frac{2}{6}=\frac{2\times 1}{3\times 2}=\frac{1}{3}$

$\therefore \text{P(not rolling a factor of 5) = 1 - P(rolling a factor of 5)}$

$\Rightarrow \text{P(not rolling a factor of 5)}=1-\frac{1}{3}$

$\Rightarrow \text{P(not rolling a factor of 5)}=\frac{3}{3}-\frac{1}{3}$

$\Rightarrow \text{P(not rolling a factor of 5)}=\frac{3-1}{3}=\frac{2}{3}$

$\therefore$ The probability of not rolling a factor of $5$ on a fair die is $\frac{2}{3}$.

Hence, option (a.) is the correct choice.