Question

The probability that a randomly chosen two-digit number in palindromic is __.

Answer 1

\[\text{probability}=\frac{\text{2 digit numbers that are palindromic}}{\text{all possible 2 digit numbers}}\]
A 2 digit number is palindromic if its digits give the same number when their order is reversed. For instance, 22 is a palindrome, but 21 is not.

The total number of 2 digits numbers is \(9\times10=90\) because the first digit cannot be a zero (i.e. only numbers 1-9) while the second digit can (i.e. numbers 0-9).

Of these numbers, there are 9 palindromes (11, 22, ..., 99), so the probability would be \(\dfrac{9}{90}\).