Question

A die has two faces each with number '$1$', three faces each with number '$2$' and one face with number '$3$'. If die is rolled once determine
(i) P(2) (ii) P(1 or 3) (iii) P(not 3)

Answer 1

Total number of faces $=6$
(i) Number faces with number ${}^{\prime }{2}^{\prime }=3$
$\therefore P\left(2\right)=\frac{3}{6}=\frac{1}{2}$

(ii) $P\left(1or3\right)=P\left(not2\right)=1-P\left(2\right)$

$\Rightarrow P\left(1or3\right)=1-\frac{1}{2}=\frac{1}{2}$

(iii) Number of faces with number ${}^{\prime }{3}^{\prime }=1$
$P\left(3\right)=\frac{1}{6}$
Thus, $P\left(not3\right)=1-P\left(3\right)=1-\frac{1}{6}=\frac{5}{6}$