1) What are the averages describing? There is necessarily a causal relationship between the average, and the thing the average describes. If this were not the case, there would be no macroscopic reliability, whatsoever.
So, for example, the time it takes for a tritium nucleus to decay. There is an average value for when those decays happen. The easiest way to calculate that average is to add up the times and divide by the number of nuclei that decayed. So, yes, there is a way of going from the times for the individual decays to the average decay time. That isn't a *causal* relationship. It is simply calculational.
But the time for the individual decays is uncaused.
2) Misinterpretation. Probability is not compatible with spontaneity.
How so? In each year, there is a .0547 probability that any given tritium nucleus will decay. There is no way to know whether or not any specific nucleus will decay or not: all such nuclei are identical. However, nothing triggers the decay when it happens, so it is spontaneous.