Yes I can flip two independent coins a finite number of times and get strings that appear to be correlated. But in the asymptotic limit the probability they are the same (or correlated at all) goes to zero. Hence, two causally unrelated things can appear dependent for finite sample sizes. But when we have infinite samples (which is the limit we assume when making statements about probabilities) we get P(a,b) = P(a)P(b).
Yes I can flip two independent coins a finite number of times and get strings that appear to be correlated. But in the asymptotic limit the probability they are the same (or correlated at all) goes to zero. Hence, two causally unrelated things can appear dependent for finite sample sizes. But when we have infinite samples (which is the limit we assume when making statements about probabilities) we get P(a,b) = P(a)P(b).