Ninety Nine Percent Doomed

You count distinct substrings of one string by storing $n = 10^5$ substring hashes in a hash set. Each hash is a single polynomial hash modulo $m = 10^9 + 9$. Any collision between two different substrings makes the count wrong.

With $\binom{n}{2}$ unordered pairs each colliding independently with probability about $1/m$, the chance that at least one pair collides is approximately

$P \approx 1 - e^{-\binom{n}{2}/m}$

Roughly what is $P$?