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If the average distance, that a molecule goes without hitting another one is [itex]l[/itex] (by the way, could you please tell me what this distance is called in english?) and [itex]x[/itex] is the distance it's already passed without hitting another molecule, is the probability, that it hits a molecule at the current distance [itex](\frac{1}{2})^{x/l}[/itex]? (taken from the assumtion, that it passes the distance [itex]l[/itex] with a 50% probability)

Is it useful (/common practice) to distribute the velocities of the molecules correspondently with the Maxwell-Boltzmann distribution or can I just give every molecule the same, average speed?

How do I proceed with the collision of two molecules? From what I've heard I want to calculate the probability that it hits another one, get a random number from 0 to 1 and find out if it hit something. But what next? How do I choose the molecule that it has hit?