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Question: Why don't offspring have all their parents inherited traits?
Answer: Good question. Each person has two copies of every chromosome (and all the genes that are on it); they inherit one from each parent, one copy via the sperm from the father and one copy via the egg from the mother. The two copies usually have subtle differences in their sequences (mutations) that cause the genes to produce different traits. Since the father and the mother also have two copies of each gene, and only one copy can end up in each sperm or egg, it is random which copy ends up in each sperm or egg cell. Since there are 23 pairs of chromosomes, there are 8,388,608 different possible combinations of chromosomes that can be created by each parent in each sperm or egg. That does not take into account something called recombination, which mixes up the DNA between the maternal and paternal copies of each chromosome during meiosis, creating an almost infinite number of possible combinations.
It is a wonder siblings look alike at all. On average, full-siblings share half of their mutations in common with each other and with each parent. Lastly some mutations are dominant over others and prevent the expression of other traits. There are many other even more complex ways genes can interact, but the few ways I have listed here make it easy to understand why you and your parents are not exactly the same.
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