Hilda Geiringer's Portrait

Hilda Geiringer was a great German mathematician from the 20th century who was a pioneer in applying the theory of relativity and statistics to different fields, such as genetics.

In order to study the eye colour of an individual, we must know that it depends on two alleles, one from the father and one from the mother, which include the genetic information of the colour to inherit.  The result obtained from combining both alleles is called a genotype, and the final eye colour, phenotype. If they receive at least one hazel allele (genotype), the individual will have hazel eyes (phenotype), while in order to have blue eyes, they would have to inherit two blue alleles. This means that the hazel allele is the dominant one, because it determines the eye colour even if it just appears once.

Let's imagine that a hazel-eyed woman has a baby with a blue-eyed man. Study the possible genotypes of the parents and complete the following table with the different genotype possibilities for the baby.

1.    How many possible combinations are there in total? How many of them are different?

2.    What eye colour will the baby have in each case?

3.    Using Laplace's rule of succession, calculate the probability of the baby having blue eyes. What is the probability of the baby having brown eyes?

4.    If they have a first child with blue eyes, what is the probability of them having a second child with blue eyes too?