Numbers that are palindromes read the same forward and backward, For example, 30203 is a five-digit palindrome. If a single number is chosen randomly from the set of all two-digit numbers, what is the probability that it will be palindromic?

1 Answer
Jason K.
Dec 6, 2017

#1/10#

Explanation:

For a two digit number to be palindromic, reading the same forward and backward, it must be a number from this set: {11, 22, 33, 44, 55, 66, 77, 88, 99}.

Now, this is where it becomes a bit of an argument about the sets. Is the number 00 considered to be a two-digit number? I've seen this handled sometimes with 00 being included in the set and sometimes without it being in the set. For this solution, I will ignore 00, along with 01, 02, and other numbers with a leading 0.

In that case, there are exactly 9 palindromes in our desired set, and there are 90 numbers from 10 to 99. Thus, the probability is #9/90 = 1/10#

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