What is your blood type? (Part 3)
The Rh-antigens classify people into Rh-positive or Rh-negative groups apart from the ABO blood system, and each of us acquires a pair of Rh-controlling genes from our parents (one from father and one from mother).
The Rh-negative individuals have 2 Rh-negative genes presented in their DNA, resulting in no Rh-antigens on the red blood cells. On the other hand, the Rh-positive gene is dominant over the negative one: if one or two Rh-positive genes are presented, that person will be Rh-positive. The persons with 1 Rh-positive gene & 1 negative gene are called carriers, for they can pass on the Rh-negative gene despite being Rh-positive. A carrier parent has a 50:50 chance of giving his or her child a Rh-positive or negative gene.
Statistically, about 16% of the European population has Rh-negative blood type.
Under ideal genetic distribution, if you meet someone in Europe, what is the chance that he or she is such a carrier?
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1 solution
This problem is related to the Hardy-Weinberg's principle, which deals with genetic distribution in the big population. The main equation used is: p + q = 1 and ( p + q ) 2 = p 2 + 2pq + q 2 = 1, where p is the proportion of the normal gene (Rh-positive) in the gene pool and q is the proportion of the affecting gene (Rh-negative). The Punnett square in the diagram above shows the 4 permutations of the p & q genes, where pq stands for the carrier stage and qq for the Rh-negative type.
Then we can substitute q 2 = 16% = 16/100 (proportion of Rh-negative Europeans).
Thus, q = 4/10 = 40%. Then p = 100% - 40% = 60%.
In other words, in all the European gene pool, 60% of the genes are Rh-positive genes and 40% are Rh-negative ones.
So we can calculate the proportion of the carriers as: 2pq = 2(60%)(40%) = 48%.
As a result, 48% of the Europeans are carriers, so there's a 48% chance for us to meet such carrier in Europe.