# Basic question about probability and measurements

Say I have a Galton box, i.e. a ball dropping on a row of solid bodies. Now I want to calculate the probability distribution of the movement of the ball based on the properties of the body (case A). For instance if I change the position of the ball the distribution might change (case B). I want to know the distribution of the ball after it has hit the body, as a function of various properties. Does it even make sense to speak of a probability distribution here? Basically what I had in mind before, is that quantum mechanics is probabilistic and that classical mechanics is deterministic. Does this mean one can actually calculate where each ball will end up, if the measurements are precise enough?

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More on a Galton box: physics.stackexchange.com/search?q=is%3Aq+galton –  Qmechanic Nov 1 '13 at 17:46

In classical physics, all the motion of the objects and the behavior after all the recoils is predictable in principle. In practice, there's always some dependence on tiny errors in the knowledge of the initial state; tiny velocities that the elements may have and the motion and rotation of the marble in particular; tiny non-uniformities in the shape of the elements, and so on. The required accuracy in the knowledge of all these things is "exponential" (the error has to be at most $\exp(-X)$ where X is a number much greater than one) if we want to be able to predict the evolution for a long time, e.g. in a tall enough Galton box.