At times in the past, red hair in humans was thought to be a recessive trait, and at other times it was thought to be a dominant trait.
a) what feature of inheritance would red hair be expected to exhibit if it were a recessive trait?
b) what features would it be expected to exhibit if it were a dominant trait?

A) If red hair were a recessive trait, it could be inherited in two ways: 1) from heterozygous parents who both carry the red hair allele (the chances of having a child with red hair would be 25%), or 2) from red haired parents who are both homozygous (100% chances of red haired offspring).

B) If red hair were a dominant trait, it could be inherited only if at least one of the parents had red hair. There's 3 variables: 1) If both parents were heterozygous, they would have a 75% chances of having red haired children; 2) if one parent were heterozygous and the other were homozygous dominant, all of their offspring would have red hair; and 3) all children would be red haired if both parent were homozygous, one dominant and the other recessive.

This exercise is an example of Mendelian inheritance which states that the genes inherited from parents are separated into gametes in equal frequency. Each parent "donate" an allele to their offspring; this allele could be physically expressed or not depending on it being dominant or recessive (this means: silent) and if the parents being homozygous or heterozygous. Heterozygous individuals have two different alleles (one dominant and one recessive), while homozygous can have either 2 dominant alleles or 2 recessive ones.