Meiosis and combinations of chromosomes

Question

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.

Answer 1

It would be right if there were no recombination (see also crossing over) and no new mutations. However, there are crossover and there are mutations and hence the calculation is wrong.

Segregation

You have solved this problem yourself. You assumed that chromosomes segregate perfectly independently which is a rather sound assumption. The probability is $\frac{1}{2^{46}}$

Recombination

Assuming a genome-wide recombination rate of 22.8 (Wang et al. 2012) and assuming that the number of recombination is Poisson distributed, then the probability of no recombination is $e^{-22.8} ≈ 1.25\cdot 10^{-10}$.

Multiply this number by $\frac{1}{2^{46}}$ and you get about $1.8 \cdot 10^{-24}$. I would note however, that the assumption that the number of crossover is Poisson distributed might not hold (even if it is how it is typically modelled)

Mutation

Now assuming a genome-wide mutation rate of 45 (Rhabari et al. 2016), and assuming that the number of mutations is Poisson distributed, then the probability of no mutation to happen is $e^{-45} ≈ 2.9 \cdot 10^{-20}$.

Hence the probability becomes $\frac{1}{2^{46}} \cdot e^{-22.8} \cdot e^{-45} ≈ 10^{-44}$.

Note that we assumed that the number of mutations and the number of crossovers are independent which is definitely wrong. If we were to know the correlation, we could make better estimates. This would bring our estimate to some higher probability.