Question

A two digit number is formed with digits 2,3,5,7,9 without repetition. What is the probability that the number formed is
(i) an odd number?
(ii) a multiple of 5?

Answer 1

Digits are $\{22,23,25,27,29,32,33,35,37,39,52,53,55,57,59,72,73,75,77,79,92,93,95,97,99\}$

$\therefore$Total digits are $25$

Odd numbers are $20$

$\therefore$ probability that an odd number is formed is

$\frac{20}{25}=\frac{4}{5}$

a multiple of $5$

Numbers which are multiple of 5 are

$\{25,35,55,75,95\}$

$\therefore$ probability of multiple of 5 is

$\frac{5}{25}=\frac{1}{5}$