Question

Two unbiased dice are rolled once. Find the probability of getting :
a) a sum $8$
b) a doublet
c) a sum greater than $8$

Answer 1

$S=\left\{\begin{array}{c}(1,1)(1,2)(1,3)(1,4)(1,5)(1,6)\\ ................................\\ (6,1)(6,2)(6,3)(6,4)(6,5)(6,6)\end{array}\right\}$
$n\left(S\right)=36$
i) Let $A$ denotes the sum being $8$.
$A\{(2,6),(3,5),(4,4),(5,3),(6,2)\}$
$n\left(A\right)=5$
$P\left(A\right)=\frac{n\left(A\right)}{n\left(S\right)}=\frac{5}{36}$
ii) Let $B$ denotes the doublet
$B=\{(1,1),(2,2),(3,3),(4,4),(5,5),(6,6)\}$
$n\left(B\right)=6$
$P\left(B\right)=\frac{n\left(B\right)}{n\left(S\right)}=\frac{6}{36}=\frac{1}{6}$
iii) Let $C$ denotes the sum greater than $8$.
$C=\{(3,6),(4,5),(4,6),(5,4),(5,5),(5,6),(6,3),(6,4),(6,5),(6,6)\}$
$n\left(C\right)=10$
$P\left(C\right)=\frac{n\left(C\right)}{n\left(S\right)}=\frac{10}{36}=\frac{5}{18}$