Probability of 8 or 9 digit sequence colliding in the same place in two 65 digit numbers I have two numbers:
3032643431333337636238613038343231383364303731376566303037663231

3861663464383131656131653461343961343364303737663565356561653361

36430373 repeats from digit 36-45 (I only extracted the 8, but the 9th matched too).
What are the chances that the same 8 digits would repeat in two 65 digit length numbers?
What are the chances that the same 9 digits would repeat in two 65 digit length numbers?
Minor Details: I extracted 8 digits from a hash(md5) that was converted to a binary string and then hex encoded to get the 65 digits.  I found the collision and was curious as to the odds.
Thanks
Edit:  As was commented, the digits must be between the 36th and 45th position.  Not elsewhere in the number.

If "repeats" means also "on the same places", as it is suggested by your example, it is simply a chance of taking a fixed 8-digit number, because the other digits are arbitrary. Hence the probability is $10^{-8}$.
You are lucky or your numbers are not uniformly distributed. :-)
