Gametes, which are sex cells, carry the alleles. Why must a gamete carry one allele (represented by a letter) from each gene? meaning, why can't a gamete carry an "hh" instead of an "hs" or an "Hh" instead of a "HS?''

A gamete carries one allele (represented by a letter) from each gene - it prevents from causing gene overload and prevents from leading to defective offspring.

Gamete or reproductive cell containing only one set of dissimilar chromosomes, or half the genetic material necessary to form a complete organism

Thus, A gamete carries one allele (represented by a letter) from each gene - it prevents from causing gene overload and prevents from leading to defective offspring.

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Explanation:

This is because a gamete will go fuse with another gamete and the sets of alleles from both will combine to form the required diploidy required for growth to a mature organism. If the gametes were diploid, then when two gametes fuse, the resulting zygote would be tetraploidy. Unless this is the natural ploidy for the organism – like in some plants – then the resulting zygote would not develop or the resulting mature organism would have abnormalities.