Single gene disorders can be encoded by either dominant or
recessive alleles. In the latter case, the affected person
usually has two healthy carrier parents, who were usually unaware
that their child could inherit a deadly or debilitating genetic condition from them.
We know from Mendel's first law that any offspring of two heterozygous carriers
has a 25% chance of inheriting a recessive disorder.
Knowing your own genotype is therefore important when deciding to have children, and
genetic screening will prove vital for preventive medicine in the coming years.
In this problem, we will consider an exercise in which we determine the probability
of an organism exhibiting each possible genotype for a factor knowing only the genotypes
of the organism's ancestors.
Problem
Figure 1. The rooted binary tree whose Newick format is (aa,((Aa,AA),AA)). Each leaf encodes the genotype of an ancestor for the given individual, which is represented by '?'.
A rooted binary tree can be used to model the pedigree of an individual.
In this case, rather than time progressing from the root to the leaves,
the tree is viewed upside down with time progressing from an individual's ancestors
(at the leaves) to the individual (at the root).
An example of a pedigree for a single factor in which only the
genotypes of ancestors are given is shown in
Figure 1.
Given: A rooted binary tree T in Newick format encoding an individual's pedigree
for a Mendelian factor whose alleles are A (dominant) and a (recessive).
Return: Three numbers between 0 and 1, corresponding to the respective probabilities that
the individual at the root of T will exhibit the "AA", "Aa" and "aa" genotypes.
