Question

An experiment consists of rolling a fair die. Find the theoretical probability of rolling a number greater than $5.$

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

Answer 1

The correct option is A $\frac{1}{6}$

$\underset{–}{\text{Given}:}$
A fair die is rolled

$\underset{–}{\text{Need to Find}:}$
Probability of rolling a number greater than $5$

Since, a fair die is rolled once,
Sample space $=\{1,2,3,4,5,6\}$

$\therefore$ Total number of possible outcomes $=6$

Rolling a number greater than $5$ is the favorable outcome, i.e.,
Favorable outcome $=\left\{6\right\}$

$\therefore$ Number of favorable outcome $=1$

Hence, the probability of rolling a number greater than $5$ is

$\text{P(a number greater than 5)}$

$=\frac{\text{Number of favorable outcome}}{\text{Total number of possible outcomes}}$

$\Rightarrow \text{P(a number greater than 5)}=\frac{1}{6}$

$\Rightarrow \text{P(a number greater than 5)}=\frac{1}{6}$

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