Basically, nuclear disintegration is probabilistic in its very nature. What it means is that one cannot say with conviction that, say, one atom kept on a table will disintegrate in, say, the next 1 minute. All one can say is that among a given sample of, say, 100 nuclei, 10% of it will disintegrate in the next 1 minute.
Nuclear disintegration follows what is known as first order kinetics which means that rate of reaction is directly proportional to the quantity of reactant present. In other words,
d/dx(C) = -k C
where C is the current concentration of reactant and k is proportionality constant.
From this calculation, what one can get is a term called half-life, which means that after this time has elapsed, half of the concentration gets disintegrated (I'm using disintegrated and reacted interchangeably, since the reaction in nuclear disintegration is disintegration).
This means that a sample of 100 atoms after one half-life would remain 50 $=100 * (1/2)^1$, which after 2 half-lives would become 25 $=100 * (1/2)^2 = 50 * (1/2)^1$ and so on...