I was pondering about the genetics of siblings. It occured to me that a pair of biological brother and sister (not brothers or sisters) could inherit completely distinct sets of chromosomes from their parents, the mathematical probability being $\frac{1}{2^{46}}$. This calculation is based on the assumption that each pair of chromosomes, upon meiosis, get separated independently of other pairs. Do you think I’m right about that? Has anyone looked into this matter? Could it be that a chromosome prefers to be accompanied by a specific chromosome (in a pair other than its own) during meiosis?
Edit: I only have a high school level understanding on this matter and I just realized that my speculation directly contradicts Mendel’s law of segregation. But as pointed out in the comment on the answer, some wiggly interaction might interfere with the assortment with some peculiar genes, although it doesn’t mean that some chromosomes are more fond of each other. Close the case.