Hopefully this’ll be interesting to a few people. I don’t claim to have come up with a definitive answer, so the solution I spoiler in the next post is only my best guess.
Premise: In the native population of one of those islands that only appear in puzzle books, some natives have big noses and some natives have tiny noses. There’s nothing in between, so it’s pretty easy to tell which is which. Some basic testing has proved that the nose size among these natives is controlled by a single dominant/recessive gene. Everybody carries two copies of the gene, either big nose or small nose. If they have both genes, whichever is dominant controls the size of nose the native shows.
36% of the population has big noses. 64% of the population has small noses.
If a ‘mixed’ couple (one has a big nose, one has a small nose) have a baby, the odds that the baby will have a big nose is around 38%, plus or minus two percent.
Based on this, can you guess if the big nose gene or small nose gene is dominant? How certain of it are you? (Or if I messed up, does the whole story fail to hold water?)
ETA: Oh, I guess my answer assumes that there’s no bias either for people with the same nose size to marry, or to seek out somebody with a different nose size; they’re pretty agnostic about it on this island.