Question

Two digits are formed from the digits $0,1,2,3,4$ where digits are not repeated. Find the probability of the events that the number so formed is a prime number.

Answer 1

Let $S$ be sample space of number formed. Then,
$S=\{10,12,13,14,20,21,23,24,30,31,32,34,40,41,42,43\}$
$n\left(S\right)=16$
Let $A$ be event of prime number. then,
$A=\{13,23,31,41,43\}$
$\therefore ,P\left(A\right)=\frac{5}{16}$