It is a complicated question of how the three different blocs or areas was drawn up, which I am no expert in, and will leave to others to answer.

But I would like to point out that the area of Northern Schleswig who voted to join Denmark in 1920 did absolutely have a Danish majority. The area, also historically called Sønderjylland, consisted of towns mostly founded by Danes, and which historically had been majority Danish like Haderslev, Aabenraa, Tønder, Sønderborg, Rødding, etc., and even with 50 years of attempts at Germanification, they had remained so by the time of voting.

In 1921 the area consisted of 163.000 people in 1921 (Iversen, 320). Iversens detailed exploration of the population of the area from 1864-1920 doesn't reveal much with regards to ethnicity though, since this was not recorded by the German government in the period, and all Danes, except for immigrants from Denmark, was automatically made citizens of Germany, but it is estimated by Hans Schultz Hansen, head of the regional archives of Sønderjylland, that only 25.000 were Germans in the area in 1920 around the time of the voting.

So it was at the time pretty much a given that this particular area would vote to join Denmark. The other two blocs, Southern Schleswig and Holstein, did have a majority Germans, even though there would still be a sizeable Danish minority in the former, and still is to this day.

Mads Iversen, "Nordslesvigs Befolkning 1864-1920", Nationaløkonomisk Tidsskrift, bind 3, Række 41, 1933, pp. 319-336.