probability that a 1000 digit number selected at random is a palindrome
Answers
If it is a one digit number, it has 100% chance to be a palindrome.
If it is a two digit number, there are 90 two digit numbers (10 to 99) and 9 of them are palindromes (11, 22, 33 etc.) so there is a 10% chance of it being a palindrome.
If it is a three digit number, there are 900 three digit numbers (100 to 999). It doesn’t matter what the middle digit is, there is a one out of 10 chance that the third digit will match the first, so 10% chance.
If it is a four digit number, the first and last digit must match (10% chance )and the second and third digits must also match (10% chance ), so there is a 1% change of a four digit number being a palidrome.
Five digit number, same as for a four digit number because the middle digit doesn’t have to match anything.