Probabilities are a great way to express the myriad intricacies and complex interactions that go into producing one particular outcome to a realistically convoluted situation rather than some other potential outcome. Because no matter how labyrinthine and tortuous the details, in the end it boils down to a specific chance that outcome A occurs, or doesn't occur.
And when it comes right down to it, frankly, that's all the players really care about. So don't bother justifying potential outcomes with scientific theories and arguments. Just set a percentage chance, and let them roll. In most cases, your simple judgement alone will be enough to assign some reasonable number. It's much easier than actually thinking about how stuff works.
But what if you're really not sure what the chance of a particular outcome should be? Some GMs may be tempted to go down the path of thinking about what's happening in the context of the game, applying a consistent set of game world physical laws, and making some sort of mathematical calculation. Do not stray to this Dark Side!
So what to do? One game (which Shall Not Be Named for reasons that will be obvious to anyone familiar with it) has a solution to this problem. If you don't know what the percentage chance is that something will happen, simply roll percentile dice! Not sure what chance that potion flask has of actually containing poison? Roll percentile dice! There, it has a 37% chance of being poison! Or if you roll 85, it has an 85% chance of being poison! Then just roll against the randomly generated probabiity to determine if the flask contains poison or not.
Mathematically astute readers will no doubt already be complaining that rolling to determine the percentage, then rolling against that percentage to see which way the question resolves is equivalent to an a priori 50.5% chance. (It's not exactly 50% because in standard gaming practice a roll equal to the chance number is considered a success in rolling that probability, not a success/fail tie. But at any rate it's close enough for our purposes here.)
The much, much, much better rolepaying game of Toon therefore takes the extremely sensible shortcut of making the Fifty Percent Rule an integral part of the game:
It is both impossible and unnecessary to think of everything before the game begins. If you're ever confronted with a totally unexpected situation or you're unsure about what to do next, use the Fifty Percent Rule: When in doubt, roll it out!
Any time you can't figure out how an NPC will react to something the characters do, or any time you don't know precisely what will happen next, reduce the situation to a Yes-No question. Are the keys to the jail cell hanging right next to the cell? Can any of the characters reach the big red button marked "Do not push"? Does the store have any carrots in stock? Are there any people on the street?
Once you've reduced the situation to a Yes-No question, roll one die. If you roll a 1, 2, or 3, the answer is "Yes". If you roll a 4, 5, or 6, the answer is "No". Shout, roll your eyes, and generally act crazy, and the players may not even notice you've just pulled something from thin air. This is a really handy rule, so don't forget to take advantage of it.
Toon is a humorous game based on playing cartoon characters, but really, this advice is solid gold no matter what game you're playing.
R2-D2: Odds of survival: 30%!
[SFX]: Rumble... crunch!
Obi-Wan: Um. I don't feel dead.
R2-D2: No, not us. My ship.
R2-D2: My poor, dead ship.
Anakin: So did we survive?
R2-D2: I dunno, probably.