Originally Posted by
DYWYPI
[...] True biases do sometimes occur (e.g., faulty equipment), but more often an apparent bias will just be a random fluke that will not allow one to predict future events (fundamental uncertainty; independence of events).
It is important to note, that the joint probability of two events occurring refers only to events that have not happened yet. With a 6-Sided dice chances of any number coming up twice in a row are: 1/6, not 1/36. This is because there are six possible ways (opportunities) of getting the same number twice in a row: (1/6) × (1/6) × 6 = 6/36 = 1/6. "The dice have no memory". ...