Question

Three dice are thrown simultaneously. Find the probability of getting the same number on all the three dice.

Answer 1

$S=\left\{\begin{array}{cc}(1,1,1),(1,1,2)& ...............(1,1,6)\\ ......................& (6,6,6)\end{array}\right\}$

$n\left(S\right)=216$
Let $A$ denotes the same number on all the three dice.
$A=\{(1,1,1),(2,2,2),(3,3,3),(4,4,4),(5,5,5,),(6,6,6)\}$
$\Rightarrow n\left(A\right)=6$
$\Rightarrow P\left(A\right)=\frac{n\left(A\right)}{n\left(S\right)}=\frac{6}{216}=\frac{1}{36}$