Question

If two cubical dice are thrown simultaneously, then find the probability of getting the sum of numbers 'more than $7$' or 'less than $7$'.

Answer 1

Total number of ways in which $2$ dice may be thrown.
$n\left(S\right)=6\times 6=36$
Event of getting a sum $7$ on the uppermost faces
$\Rightarrow n\left(E\right)=\left\{\right(1,6),(2,5),(3,4),(4,3),(5,2),(6,1)$
$n\left(E\right)=6$
$\therefore$ The probability of getting a sum $7$
$P\left(A\right)=\frac{n\left(E\right)}{n\left(S\right)}$
$=\frac{6}{36}$
$=\frac{1}{6}$

The probability of obtaining a sum which is either greater or less than $7$ will be complementary to the probability of getting the sum of exactly $7$.
$P\left(A^{\prime }\right)=1-P\left(A\right)$
$=1-\frac{1}{6}=\frac{5}{6}$.