Question: In humans (and many other organisms), genes come in pairs. A certain gene comes in two types (alleles): type a and type A. The genotype of a person for that gene is the types of the two genes in the pair: AA, Aa, or aa (aA is equivalent to Aa). Assume that the Hardy-Weinberg law applies here, which means that the frequencies of AA, Aa, aa in the population are p2, 2p(1 - p),(1 - p)2 respectively, for some p with 0
(a) Find the probabilities of each possible genotype (AA, Aa, aa) for a child of two random parents. Explain what this says about stability of the Hardy-Weinberg law from one generation to the next.
(b) A person of type AA or aa is called homozygous (for the gene under consideration), and a person of type Aa is called heterozygous (for that gene). Find the probability that a child is homozygous, given that both parents are homozygous. Also, find the probability that a child is heterozygous, given that both parents are heterozygous.
(c) Suppose that having genotype aa results in a distinctive physical characteristic, so it is easy to tell by looking at someone whether or not they have that genotype. A mother and father, neither of whom are of type aa, have a child. The child is also not of type aa. Given this information, find the probability that the child is heterozygous.