Question

A two digit number is to be formed from the digits $0,1,2,3,4$. Repetition of the digits is allowed. Find the probability that the number so formed is $a$.
1) Prime number
2) Multiple of $4$
3) Multiple of $11$.

Answer 1

Numbers are:

$10,11,12,13,14,20,21,22,23,24,30,31,32,33,34,40,41,42,43,44$

1) Prime number

$11,13,23,29,31,37,41,43$

$P=\frac{8}{20}$

2)Multiple of 4

$12,16,20,24,28,32,36,40,44$

$P=\frac{9}{20}$

3)Multiple of 11

$11,22,33,44$

$P=\frac{4}{20}$