Student or Learner
Since "by chance" refers to "by accident" or "by luck", of course you cannot predict anything by chance (if you indeed hit it by chance, that is only a luck, nothing to do with your power of predicting).
So "could not be predicted by chance" makes no sense in my ears.
But no doubt I believe the author makes sense.
How to properly understand "could not be predicted by chance"?
The Science of Things That Aren't So
By Bruce Chassy & Henry I. Miller
Chemistry Nobel Laureate Irving Langmuir related in a landmark 1953 speech his visit to the laboratory of J.B. Rhine at Duke University, where Rhine was claiming results of ESP experiments that could not be predicted by chance, and which he ascribed to psychic phenomena. Langmuir discovered that Rhine was only selectively counting the data in his experiments, omitting the results from those he believed were guessing in order to humiliate him.
The evidence? Rhine felt that some of the scores were too low to have occurred by chance, and that it would, therefore, actually be misleading to include them.