You have to make a distinction between what happens on a microscopic (the atom) and macroscopic (decay of an amount of atoms) level. On a microscopic level you

You have to make a distinction between what happens on a microscopic (the atom) and macroscopic (decay of an amount of atoms) level. On a microscopic level you need a stochastic model to describe the decay of an atom. With a lot of atoms (I don't remember thr tipping point) you can use a deterministic model, which is the mean of of the distribution of the stochastic model.