Will my descendants have blue eyes?
Personatges:
Tema: Probability
Competències
Competència Matemàtica, en ciència, tecnologia i enginyeria
Competència personal, social i aprendre a aprendre
Competència en consciència i expressions culturals
Matèries i cursos per Sistema Educatiu
Espanya > Matemàtiques > 2n ESO > Sentit estocàstic
Espanya > Matemàtiques > 2n ESO > Sentit socioafectiu
Espanya > Matemàtiques > 3r ESO > Sentit estocàstic
Espanya > Matemàtiques > 3r ESO > Sentit socioafectiu
Espanya > Matemàtiques > 4t(A) ESO > Sentit estocàstic
Espanya > Matemàtiques > 4t(A) ESO > Sentit socioafectiu
Espanya > Matemàtiques > 4t(B) ESO > Sentit estocàstic
Espanya > Matemàtiques > 4t(B) ESO > Sentit socioafectiu
Enunciat
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. Besides, if an individual has just one hazel allele, they will have hazel eyes, but in order to have blue eyes, we need 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 woman with a hazel and a blue allele (and, therefore, with hazel eyes) has a baby with a blue-eyed man (that is, someone with two blue alleles). In the following table you will find all the possibilities considering what each one of them might pass on to their offspring.
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?
Observacions i 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.
-It can be used in applied mathematics in 3rd of ESO.
-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).
Descripció
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.