Question

Two digit numbers are formed from the digits $0,1,2,3,4$ where digits are not repeated. Find the probability of the events that
(1) the number formed is an even number.
(2) the number formed is prime number.

Answer 1

Two-digit numbers are formed from the digits $0,1,2,3,4$ without repeating the digits.
$\therefore$ Sample space $S=\{10,12,13,14,20,21,23,24,31,32,34,40,41,42,43\}$
$\therefore n\left(S\right)=16$
(1) Let $A$ be the event of getting an even number.
$A=\{10,12,14,20,24,30,32,34,40,42\}$
$\therefore n\left(A\right)=10$
Probability, $P\left(A\right)=\frac{n\left(A\right)}{n\left(S\right)}=\frac{10}{16}=\frac{5}{8}$
(2) Let $B$ the event of getting a prime number.
$B=\{13,23,31,41,43\}$
$\therefore n\left(B\right)=5$
Probability, $P\left(B\right)=\frac{n\left(B\right)}{n\left(S\right)}=\frac{5}{16}$