Is it valid to consider a rare event more likely to have been produced by chance if previous trials exist?
Suppose John tosses a coin and thinks his mind can cause it to land on heads. He tosses the coin and it lands on heads 10 straight times. Suppose, for the sake of this example, that the coin couldn’t have been rigged, or that its probability is extremely low, say 1 in 10^50.
I am now tasked with figuring out whether his mind affected the result or whether it was chance. Personally, I would not believe it. The reason I wouldn’t is because I sort of imagine previous trials. I imagine that in human history, people must have tossed millions of coins. It is not surprising that eventually, at least one person would land a coin on heads 10 times. Note that in this case this isn’t exactly analogous to the inverse gambler’s fallacy. The inverse gambler’s fallacy suggests that previous trials must have occurred because a rare event occurred. But this isn’t what I’m suggesting.
I am not proposing that previous trials must have existed BECAUSE this rare event occurred. I am using my reasonable knowledge of previous trials having occurred to infer instead that this rare event shouldn’t be that surprising.
Is this reasoning sound? And what here can be considered a previous trial in the first place? For example, imagine I created a new kind of coin. This coin had special attributes and was a type of coin that never existed before, but yet still, could only land on heads or tails. If John now landed this coin on heads 10 times, my intuition/mind may not consider previous trials of coins (which are of a different type) as relevant.
This type of coin in my head, after all, had not been tossed before. What if, instead of a coin, it was a different object, and yet produced one of two results with a 50% chance, and John instead “tossed” that object? Does this make a difference?
My general question is twofold if any of this sounds confusing:
a) should previous trials affect whether or not one thinks the current trial is produced by chance?
b) what constitutes as previous trials? How “similar” must the previous trials be as an event to the current trial to be counted? What should this similarity be based on?