why do non-sister chromatids cross over instead of sister chromatid
Think of what the purpose of crossing over is - to increase genetic diversity. Sister chromatids are genetically identical (there are two copies of the same chromosome attached to one another), so if they cross over with each other, the pieces of DNA that are swapped will be identical and so the chromosomes will not have changed genetically after crossing over is complete. Crossing over occurs between HOMOLOGOUS (non-sister) chromosomes. This way, the chromosomes end up mixing and matching allele combinations and so increase the potential for genetic diversity in the offspring.
@matt101 There is no purpose of crossing over. There is not force directing these events to create a desired outcome. Also, sister chromatids do undergo crossing over events, but because they are virtually 100% identical, it does not matter.
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