our ability to determine

Suppose that we put one gram of radium in a time vault & leave it there for 1600 years, when we return we will find that only half a gram of radium is left.

This phenomenon is termed by physicists as 'half life'. Radium atoms will naturally disintegrate such that only half of them would remain behind every 1600 years.
If we put that half gram back in the vault for another 1600 years, only 1/4 of the original would remain.

Every 1600 years half of the radium atoms would just disappear.
This is familiar to most of us, as this is what we have learned in high school.

We know this as a statistical fact, that every 1600 years, half of the original radium atoms would just disappear, but we don't know which half or which of the actual radium atoms would disappear.
We cannot pinpoint which would remain or which would disintegrate.
We can only state that half of them would disintegrate in 1600 years.

The curious thing is that if all radium of the original one gram atoms are similar what makes half of them to remain and the other half to disintegrate. As such they the radium atoms are all similar, which is why we can't determine which ones would remain and which would disintegrate.

The fact is that the study of quantum mechanics can only determine the end effect, but cannot determine which constituents would meet that end effect as explained in the example above. To that effect quantum mechanics provides us just statistical fact about the effect and not what actually caused the effect.

Ergo it ushers in the realm of probability. Since it is limited in determining which atom of radium in a gram would disintegrate, it states that every atom of radium in that 1 gram of radium has a 50% probability to disintegrate in 1600 years.

And so our knowledge about quantum mechanics - the most profound discovery in the 20th century is that it can gives us an ability to correlate observed phenomena with theory in aggregation but not in individual basis, as we don't know how each atom would act - that is to disintegrate or remain, but we do know as a whole 50% of the radium atoms would disintegrate.