Probability

Are statements about probability universal truths? Is it possible to conceive of a universe in which a fair coin lands heads 75% and tails 25% of the time?

Comments

There are at least two possibilities you might be getting at:

First, it's surely possiblle for an evenly weighted coin (even in this universe) to come up heads 75% of the time over the course of its life. Suppose I mint a coin; it comes up tails just one of the four times I flip it; and then I melt it.

Second, it's conceptually possible for a universe to contain laws or supernatural agents that ensure that evenly weighted coins come up heads 75% of the time. I think it would be misleading to call evenly weighted coins "fair" in this alternative universe, however.

Both these situations seem possible to me, although if they obtain only in different possible universes then it might remain a "universal truth" that evenly weighted coins land heads 50% of the time. In any case, we should recognize that coin "flipping" and "landing" only make sense where there is a reasonable amount of gravity. And for all I know there may be places in this universe where, for example, the uneven shape of evenly weighted coins makes them "land" heads up more often than not.

In answer to the question, whether a fair coin's flips might approach 75% heads and 25% tails, I'd like to say No. For the trivial reason that approaching 50% heads/50% tails is just what we mean by "fair coin."

A fair coin may land "heads" over and over again, as we all know. As the number of tosses increases without bound, the likelihood of the coin's landing exclusively on "heads" becomes arbitrarily small. So in the limit, the likelihood of its landing "heads" over and over (or even 75% of the time) is zero. Nevertheless, it is possible (where a "fair" coin, by definition, has a 50% chance of landing heads and a 50% chance of landing tails).

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