Question

A fair die is thrown. The probability of not rolling a factor of $4$ is .

• A. $\frac{1}{2}$
• B. $\frac{1}{3}$
• C. $\frac{1}{4}$

Answer 1

The correct option is A $\frac{1}{2}$

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

The numbers on the die that are factors of $4$ are $1,2\text{and}4.$

$\therefore$ On rolling a factor of $4$, the number of favorable outcomes is $3$.

Now,
$\text{P(rolling a factor of 4)}=\frac{\text{Number of numbers on die which are factor of 4}}{\text{Total number of numbers on die}}$

$\Rightarrow \text{P(rolling a factor of 4)}=\frac{3}{6}=\frac{3\times 1}{3\times 2}=\frac{1}{2}$

$\therefore \text{P(not rolling a factor of 4) = 1 - P(rolling a factor of 4)}$

$\Rightarrow \text{P(not rolling a factor of 4)}=1-\frac{1}{2}$

$\Rightarrow \text{P(not rolling a factor of 4)}=\frac{2}{2}-\frac{1}{2}$

$\Rightarrow \text{P(not rolling a factor of 4)}=\frac{2-1}{2}=\frac{1}{2}$

$\therefore$ The probability of not rolling a factor of $4$ on a fair die is $\frac{1}{2}$.