Why did I inherit blue eyes?
Characters:
Theme: Probability
Competencies
Mathematical competence in science, technology and engineering
Personal, social and learning to learn competence
Competence in cultural awareness and expressions
Subjects and year by Educational System
Spain > Mathematics > 4th(B) ESO > Stochastic sense
Spain > Mathematics > 4th(B) ESO > Socio-affective sense
Enunciation
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?
Observations and context
- This is a difficult activity, considering it needs some background on genetics. It is important that the table is explained well and that students have help in completing the process of calculating all possible combinations and finding out the eye colour. It can be studied, of course, in biology.
- She was contemporary with many other great female mathematicians and physicians: Emmy Noether (1982-1935), who made relevant contributions to physics theory and abstract algebra; Mileva Maric (1875-1948), Albert Einstein's wife, who worked alongside him in the theory of relativity; Marie Curie (1867-1934), pioneer in the field of radioactivity and two-time receiver of the Nobel prize; Tatiana Ehrenfest-Afanassjewa (1876-1964), a mathematician and physician who worked in mechanic statistics.
- Some of her predecessors were important mathematicians and science educators, like Charlotte Angas Scott (1838-1931), a specialist in algebra and geometry and advocate of women's incorporation into universities; Nicole Lepaute (1723-1788); Maria Gaetana Agnesi (1718-1799), mathematician specialist in differential and integral calculus; Elena Lucrezia Cornaro Piscopia (1646-1684); Maria Cunitz (1610-1664); and Sophia Brahe (1556-1643).
- She worked in applied mathematics in particular, applying probability techniques to the study of genetics, as Florence Nightingale (1820-1919) did before her, when she applied statistics in her job as a nurse; or as Maria Goeppert-Mayer (1906-1972) did later, when she applied probability calculations in her study of particle physics.
- Other contemporary figures of Hilda Geiringer are engineer and architect Anna Wagner (1889-1943); the inventors Beulah Louise Henry, nicknamed Lady Edison (1887-1973), and Maria Beasley (1847-1904); the teacher Rosa Sensat i Vilà (1873-1961); the writer Sidonie-Gabrielle Colette (1873-1954); Maria Orosa (1893-1945), scientist specialized in nutrition and captain of the Filipino army during the Second World War; or the composer Ljubica Marić (1909-2003).
Description
In this activity, we will use Laplace's rule of succession to calculate the probability of a baby having blue or brown eyes, keeping in mind the rules of genetics and conditional probability.