WC 5.1 Palindrome Probability

What is the probability that a randomly drawn n-digit number is a palindrome?

For example, for a 1 digit number(n=1), every number is a palindrome. Thus probability of a palindrome is 10/10 which is reducible to 1/1. For a 2 digit number, 11, 22,..99 are palindromes. There are thus 9/90 palindromes (reduced fraction: 1/10).

Find the probability of a 10-digit palindrome. Reduce this fraction to the lowest terms and state your answer to be the product of numerator and denominator.

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