Guild Wars 2

I level up all my characters with EoTM so I have quite a few Embroidered Belt Pouches. Do these have a chance of dropping a precursor? I know it will be very unlikely but I just want to know if there is even a slim chance to get one.

a friend of mine pulled the hunter from one so id say yea they do

Yes, as long as you open them on a character that can get level 80 exotics as normal drops, you have a small chance at getting a precursor from those champ bags.

Any champ bag has a (small) chance at a precursor.
My understanding is that there’s a pool of general exotics which includes precursors, and a few exclusive exotics for each bag type.

The game rolls on a table to determine what loot type you get. If you get the random exotic, it picks randomly from the entire group of eligible exotics.
There may be a weighting aspect there too, so that precursors occur less frequently than the average.

similarly, a week ago, Zap dropped for me from the Airport champ (from killing him, not the bag or chest)

Any time an exotic random weapon might drop, there’s a remote chance it could be a precursor.