In the revamped recent XCom games by Firaxis, what happens is that the game produces a "seed list", and generates all the random numbers between 0 and 100 in a long, long list. When it needs to use a number it takes the next one off the stack to compare to your action, be it firing a weapon, capturing an alien etc.
In the first game, the stack was fixed for the duration of the game. So even if you reloaded and attempt the action again, it would always be the same outcome. There was an option in the second game to "scum save", which meant when you reloaded a save game, it would regenerate the random number list. This did make completing Impossible difficulty a little easier!