Question

A die is thrown, Find the probability of the following events:
(1) Getting prime numbers on the upper surface
(2) Getting a number which is less than $7$ on upper surface

Answer 1

A die is thrown
$\left(S\right)=\{1,2,3,4,5,6\}$
$n\left(S\right)=6$
(1) Let $A$ be in the event of getting a prime number
$A=\{2,3,5\}$
$n\left(A\right)=3$
$\therefore$ $P\left(A\right)=\frac{n\left(A\right)}{n\left(S\right)}$
$=\frac{3}{6}$
$=\frac{1}{2}$
(2) Let $B$ be an event of getting a number less than $7$
$B=\{1,2,3,4,5,6\}$
$\therefore$ $n\left(B\right)=6$
$\therefore$ $P\left(B\right)=\frac{n\left(B\right)}{n\left(S\right)}$
$=\frac{6}{6}=1$
$\therefore$ $P\left(A\right)=\frac{1}{2},P\left(B\right)=1$