Whole chromosome preservation through generations

[nobahar]

Hello!
I have a peculiar question concerning, as the title states, whole chromosome preservation through the generations.
I'll include my reasoning in case you need to point out any discrepancies.
During meiosis, crossing over occurs between non-sister chromatids. Two of the chromatids from homologous chromosomes are therefore preserved, although they will separate into different gametes. The chances of you obtaining a complete chromosome that has not been subjected to crossing over is \frac{1}{4} for anyone chromosome. Am I correct to assume then, that the chances of your sharing anyone complete chromosome in common with an ancestor is (\frac{1}{4})^n? Where n is the number of generations you work backwards?
Thanks in advance.

 

[nobahar]

Aplogies, I think it should be \frac{1}{2}. As an 'intact' (i.e. passed on from the previous generation without being subjected to crossing over) chromosome is an 'intact' chromosome, and I suppose I shouldn't discriminate against the two homolgous chromosomes.
Can anyone advance on this? Basically, I am interested in the preservation of allele combinations. From this reasoning, it doesn't seem that unlikely that an enitire chromosome would be preserved, and therefore all the alleles for the different genes that were togeather in the previous generation are togeather again in the next.