Question: I wondered this since my teacher told us about half life of radioactive materials back in school. It seems intuitive to me to think this way, but I wonder if there's a deeper explanation which proves me wrong.

When many atoms are involved, half life can statistically hold, but since decaying of an individual atom is completely random and stateless, can't all the atoms in a 1 kg of matter just decide to decay in the next minute, even if the probability of this event occurring is extremely small?

Answer: 
The answer is 'no'. This 'no' is on the same level like:

* Can it happen that you float for 15 minutes in the middle of your room. (Statistical mechanics tells technically yes, but again with a for all practical purposes zero probability)
* Can you put a monkey in front of a typewriter and get Shakespeare novels out of it?
* Can you walk through a solid wall (non zero tunnel probability due to quantum mechanics)
To understand this, you need to see what triggers a nuclear decay. The answer is a beautiful example of quantum mechanical behavior. Nothing triggers it. It is just that the world is fundamentally quantum mechanical, and probabilistic.

> 
> All the other answers that "no, there is no triggering event, it just happens, quantum mechanics is like that" are perfectly right.
> 
> 
> 

[What happens before a radioactive element decays?](https://physics.stackexchange.com/questions/164665/what-happens-before-a-radioactive-element-decays/164679#164679)

All you can do is calculate the probabilities.

So the answer to your question is, that yes, there is a non-zero probability for the material to decay in the next minute.

But your question is more about if there is a chance that all the atoms in the material decay simultaneously in the next minute. And the answer is again yes, there is a non-zero probability for that to happen, but it just happens so that the probability is so little, that even on giant timescales like the age of our universe, there is very little probability for us to observe that to happen.