So I have taken an introductory level quantum physics and am currently taking an introductory level probability class. Then this simple scenario came up:
Given a fair coin that has been tossed 100 times, each time landing heads, would it be more likely that that the next coin flip be tails or heads?
I can see that since the event is independent by definition, then the probability would be even for both heads and tails:
$$P(h | 100 h) = P(t | 100 h)$$
But would this differ in a quantum mechanical standpoint? I have a feeling that $P(h | 100 h) < P(t | 100 h)$ because of the push towards equilibrium in the entropy of the system. Am I wrong to think this way?
FOLLOW UP: (turning out to be more of a statistical problem possibly?)
Something the around the "equilibrium only exists in the infinite-time limit" idea is what I'm getting hitched on.
The proportion of head to tails is 1 to 1 as number of trails approach infinity (this is a fact correct?). Therefore, if this must be the case, mustn't there be an enacting "force" per say that causes this state of being to (admitted unreachable, but technically eventual) case? Or is this thought process just illegitimate simple because the state exist on at the infinity case?