Since quantum processes have defined probabilities, doesn’t that indicate an underlying defined mechanism?

Say I ask my friend to generate any set of random numbers for me, and all of his numbers are from 1 - 6, with a roughly even 1:6 distribution of numbers, I might infer that he could be using a 6 sided die to generate his numbers. Now if you look at radioactive materials that have different half lives, doesn't it indicate that there is some kind of underlying mechanism that gives them defined half lives? I understand that you can never know which atom will decay next, just like you can never know which number the die will land on, but you can be pretty sure that you will never roll a 10 on a 6 sided die. Why then is probability accepted as the most basic level of "incidence" in a quantum system? Shouldn't there be something underlying that causes certain quantum processes to have certain probabilities, just like my friend's 6 sided die underlies the "random" numbers he's giving me, all from 1-6?