My question is in part about language and in part about the nature of causality. I have noticed that some persons use the phrases "at random" or "by chance" in ways that make no sense to me. For instance, someone might claim that a coin which is flipped lands heads up "by chance" or that complex weather phenomena occur "at random." When pressed on what this means, they usually respond that the coin landed heads up for no reason; it just as easily have been tails up. Surely this isn't true nor is it what they genuinely mean, is it? The side on which coins land is due to weight distribution, pressure, wind, and a handful of simple mechanical principles and weather phenomena are highly complex systems that operate by way of long causal chains, but neither of them happen without any reason at all. Do these phrases really just mean, "this outcome could not be predicted because I don't have the data?" Nothing really occurs *by way of chance*, but we simply look back on outcomes that couldn't be anticipated...

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?

If I say, "the probability of landing heads in a coin toss is 50%," have I made a mathematical statement or a scientific one?

Does the word 'chance' (or 'accident', 'luck', or 'random') refer to the absence of causation, or does it express our ignorance of causation? Equally, does the word 'infinite' refer to the unlimited, or to our ignorance of limits?