Question

A die is thrown once. Find the probability of getting a number lying between $2$ and $6$.

Answer 1

We have,

Possible numbers of events on throwing a dice$=6$
Numbers lying between $2$ and $6=3,4,\mathrm{and}5$

Favourable number of outcomes$=3$

$\begin{array}{rcl}\mathrm{Probability}\mathrm{that}\mathrm{a}\mathrm{number}\mathrm{between}2\mathrm{and}6& =& \frac{\mathrm{Number}\mathrm{of}\mathrm{favourable}\mathrm{outcomes}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{outcomes}}\\ & =& \frac{3}{6}\\ & & \mathrm{Dividing}\mathrm{numerator}\mathrm{and}\mathrm{denominator}\mathrm{by}3\\ & =& \frac{1}{2}\end{array}$

Hence, probability of getting a number lying between $2$ and $6$ is $\frac{1}{2}$.