Depends on how that password is stored. Mostly.
Your alphabet, lowercase + uppercase + digits + symbols, has 72 characters. There are 72 ways to pick the first character of your password, 72 ways to pick the second, etc. So there are 72 to the 25th power possible passwords, about 7.5 times 10 to the 46th (about 7 followed by 46 zeroes).
That's fewer possibilities than the number of atoms in the universe and fewer possibilities than the ways you can order a deck of cards, but if a computer can calculate one hash per nanosecond, it'd take about ... well, more millennia than I know the words for. Even if we're talking about a cluster of GPU machines, it's effectively forever. Unless you had some infinite improbability drive (like a quantum computer?) and you guess correctly on the first try.
So what did you use to generate the random password? Did you use your favorite programming language's pseudo-random number generator? Remember, "anyone who attempts to generate random numbers by deterministic means is, of course, living in a state of sin" (John von Neumann). A bad random number generator might only have 2^32 possibilities.
Let's put that aside. It's unlikely that the hacker knows which random number generator you used. It's much more likely that the company storing your passwords is not storing them securely. Passwords should not be stored, ever. Instead, the company should store a hashcode. The hashing algorithm should be like the butterfly effect -- a tiny change in the password produces an unpredictable difference in the hashcode. Unfortunately, many older hashing algorithms, like MD5, are predictable. A hacker can find an MD5 collision -- not your password, but one that hashes to the same hashcode -- within minutes.
There's more to it, but my advice is NEVER rely on password security by itself. If you care about your security, then use 2-factor authentication or physical security in combination with password protection.
Edit: Am I incorrect? I see there was a downvote. Please educate me.