although the per turn and per resource chances are slim, it's pretty rare that you don't pop a resource in a game IMHO.
Then again, I work a lot of mines.
let's say you have 12 cities.
each (on average) working 3 mines.
that makes 36 mines.
what resources can you get?
let's say you're in the middle of the game so you can see copper and iron, but not coal and not aluminium.
- gold
- silver
- gems
- copper
- iron
= 5 different resources you can discover.
so the maths are for each turn, (1-0,0001)^(5*36) = 0,982160 : the chance you don't pop a resource on a given turn.
let's play normal speed = 500 turns.
(1-0,0001)^(5*36*500)=0,000123= 0,0123% : the chance you don't pop a resource in a full length normal speed game.
Convinced?
to be totally correct, you'd need to make a difference on the number of mines effecticely worked, and on the visible resources on a given turn.