Question

A die is thrown. Find the probability of getting a number greater than $3$.

Answer 1

Find the sample space and then find the probability

The sample space of the given experiment is given by,

$\mathrm{S}=\left\{1,2,3,4,5,6\right\}$

Let $\mathrm{C}$ be the event of getting a number greater than $3$.

$\Rightarrow \mathrm{C}=\left\{4,5,6\right\}$

$\therefore \mathrm{P}\left(\mathrm{C}\right)=\frac{\mathrm{Number}\mathrm{of}\mathrm{outcomes}\mathrm{favourable}\mathrm{to}\mathrm{C}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{possible}\mathrm{outcomes}}=\frac{\mathrm{n}\left(\mathrm{C}\right)}{\mathrm{n}\left(\mathrm{S}\right)}=\frac{3}{6}=\frac{1}{2}$

Hence, the probabilities of getting a number greater than $3$ is $\frac{\mathbf{1}}{\mathbf{2}}$.