Question

An unbiased die is thrown, what is the probability of getting
$\left(i\right)$ an even number of a multiple of $3$
$\left(ii\right)$ a number $3$ or $4$
$\left(iii\right)$ a number greater than $3$

Answer 1

In a single throw of a dice, we get $1,2,3,4,5$ or $6$.
Number of total outcomes $n\left(S\right)=6$
Probability of an event$\left(A\right)$ is
$P\left(A\right)=\frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}=\frac{n\left(A\right)}{n\left(S\right)}$, Where $S$ is sample space.

$\left(i\right)$ Even numbers multiple of $3$ are $3,6$
Favourable no. of outcomes $n\left(A\right)=2$
Required probability $P\left(A\right)=\frac{2}{6}$
$\therefore P\left(A\right)=\frac{1}{3}$

$\left(ii\right)$ a number $3$ or $4$
Favourable no. of outcomes $n\left(A\right)=2$
$P\left(A\right)=\frac{2}{6}$
$\therefore P\left(A\right)=\frac{1}{3}$

$\left(iii\right)$ number greater than $3$ are $4,5,6$
Favourable no. of outcomes $n\left(A\right)=3$
$P\left(A\right)=\frac{3}{6}$
$\therefore P\left(A\right)=\frac{1}{2}$