Is radioactive decay really random?

Radioactive decay is a stochastic (i.e. random) process at the level of single atoms, in that, according to quantum theory, it is impossible to predict when a particular atom will decay, regardless of how long the atom has existed. read more

The randomicity of radioactive decay refers to the variations in instantaneous decay rate (e.g., decays in a short time interval) relative to the average decay rate. The number of radioactive nuclei divided by the decay rate is a constant equal to the mean lifetime. read more

A decay process can be both spontaneous and random, but only one of these two options touches on the statistical nature of decay. There's a small bit in the introductory paragraph of the WP page on radioactive decay. read more