(I am not sure if the rules of quantum mechanics (e.g. requiring probability to be conserved will poke holes in the following (possibly hypothetical?) scenario (marked by *) that aims to better illustrate the example)
In ordinary quantum measurements, e.g. check if an electron is spin up or down, you get a bunch of outcomes (a sequences of ups and downs) when you measure an ensemble of them. Quantum mechanics then told you the probability of giving spin up and downs via the $|\psi|^2$, but due to the random nature of decoherence, you cannot predict in advance which eigenstate will the stat…