How can the random distribution of alleles result in a predictable ratio?

Phenotypically and genotypically there are only two different ratios. If you think of a Punett square ...

You could say that a pea plant with the trait for the dominant color green (G) could also carry the recessive trait for yellow (g). So let's say you mate a dominant green, (Gg) with another dominant green, (Gg). You would get 1 (GG), 2 (Gg) and 2 (gg).

Phenotypically (as in physical traitwise), the ratio is 3:1 because you have 3 green colored peas and one yellow.

Genotypically (as in traitwise), the ratio is 1:2:1, because you have 1 (GG), 2 (Gg) and 1 (gg).

So although it's random, for any specific trait there are only 4 different outcomes.