Assume a sperm has penetrated a polar body and their nuclei fuse. why would it be unlikely for the resulting cell to develop into a healthy embryo.

Polar bodies are considered byproducts of oogenesis. They are lacking cytoplasm and are much smaller than a regular egg cell. Typically they disintegrate after meiosis. It is unlikely for the resulting zygote to become a healthy embryo because the polar body was never meant to get fertilized. Therefore it is most likely lacking nutrients, and does not have the necessary resources for a healthy baby to develop.
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