I was looking a bit at the connection between singularities of complex algebraic varieties and exotic spheres. I find it quite remarkable that you can obtain all 28 differentiable structures on the 7 sphere by intersecting a small sphere with some very innocent looking algebraic variety. It makes me wonder how common that is: if you take a "random" algebraic variety with a singularity at the origin in $\mathbb{C}^5$, and intersect it with a small sphere, what are the chances you get an exotic structure on the 7 sphere? Are some smooth structures more likely to appear than others? Has anyone actually computed probabilities?