What justification is there for a 50% probability of Hh and 50% probability of HH. It's one of the most common logical fallacies in probability; because you have two possibility, people somehow assume that the probability of each situation must be 50%.
You can, however, justify saying that nearly all people with Huntington's disease are Hh. We know that Huntington's disease is a rare genetic disorder. Let's assume that Huntington's affects 1 person per 100 people (the real figure is about 1 person per 10,000 people of European descent). Therefore, 99% of people have genotype hh. Assuming that the population is in Hardy-Weinberg equilibrium (which is fairly valid since the HD phenotype doesn't show up until after one reaches reproductive age). This means that:
p2 = 0.99, and
p = 0.99499
where p is the prevalence of the h allele in the population. Therefore:
q = 1-p = 0.00501
Therefore, we can find the fraction of the population that are heterozygous, f(Hh), and the fraction of the population that are homozygotes, f(HH):
f(Hh) = 2pq = 2(0.99499)(0.00501) = 0.00997
f(HH) = q2 = (0.00501)2 = 2.51x10-5
So, among the people with Huntington's disease, the probability that an afflicted individual is heterozygous, f(Hh|Huntingtions), and the probability that an afflicted individual is homozgous, f(HH|Huntingtons), are:
f(Hh|Huntingtons) = 0.00997/.01 = 0.997
f(HH|Huntingtons) = 2.51x10-5/0.01 = 0.00251
In our example, 99.7% of the people with our "rare" disorder are heterozygotes and we can pretty safely ignore the population of homozygotes.