Statistical probablity is the only thing we can know exactly.Often students get bogged down in the fact that they don't "understand" how and why radioactive elements decay and miss the whole point of this exercise.Radioactivity and radioactive decay are spontaneous processes.
Not only does it decay by giving off energy and matter, but it also decays at a rate that is characteristic to itself.
Consider the following reaction: A D E The effect of isotopic substitution of reactant A is expressed as the ratio of rate constants kl/kh, where the superscripts l and h represent reactions in which the molecules of reactant A contain light and heavy isotopes.
Any such substitution modifies the reaction rate significantly.
Since radio active rays are coming out of the nucleus, the nucleus will change and can become another element.
So the atom after giving out radiation changes to some other atom or even element.