If we leave out the math equations how would explain the reason why the decay of a radioactive element is based on probability ?
If say the decay was truly a random event for each atom then would that not mean that its creation of new information (the order in which individual atoms decay) that didn't already exist in the universe ?
(0) It is a truly random event. Period.
(1) A radioactive atom (nucleus, really) follow Fermi's Golden Rule. It says "that the transition rate is proportional to the strength of the coupling between the initial and final states factored by the density of final states available to the system".
Let's say the coupling between the initial and final states is constant. Let's also say that the density of final states is constant. (Note: this is not always the case, as their are stable atoms that are unstable ions--the Coulomb energy blocks the final states for the neutral atom. There is also research into environmental effects--temperature and density--affecting decay rate. Of course, the inverse beta decay in neutron star formation is an extreme example).
Anyway, with the constant assumption, the the transition rate is fixed. This means that in any short period of time, there is some probability of decaying, which remains constant until the decay. That's how is how the system become probabilistic. Moreover, if you do the math you'll see that you can define a half-life, which is the time period over which an decay has a 50% chance of occurring. It is important to note that this is constant and stays constant. If you make a uranium-238 atom in a reactor today, it has the same probability of decaying by tomorrow as a U238 atom you dig out of the ground--even though the latter was made in a supernova billions of years ago.
(2) I am going to defer on the question of what is the entropy of a random sequence, esp. w/o math. However, I will posit that all possible orderings have equal likelihood, so there is no information in the ordering. Moreover, following the example in (1), since all U238 are indistinguishable--can you even define an order?