Thumbtacks
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 > 1r ESO > Sentit estocàstic
Espanya > Matemàtiques > 1r ESO > Sentit socioafectiu
Enunciat
Maria Goeppert was a German physicist. She received the Nobel Prize in Physics in 1963 for the discovery of nuclear orbital structure.
She graduated in 1930 using in her thesis the calculus of probabilities to analyse the orbit of the electron.
We are going to study the random experiment that consists of throwing a thumbtack and observing if it lands “point up” or “point down”.
a) Which of the two outcomes do you think is more likely to occur?
b) Check if what you have thought is correct by throwing 100 thumbtacks (or one thumbtack 100 times) and complete the following table.
| Possible results | Count | Absolute frequency | Relative frequency |
| Point up | |||
| Point down |
c) Having performed the experiment, which of the two outcomes do you now think is more likely to occur?
d) We are going to share the results obtained by the whole class, filling in the following table.
| Nº | 100 | 200 | 300 | 400 | 500 | 500 | 700 | |||||||
| af | rf | af | rf | af | rf | af | rf | af | rf | af | rf | af | rf | |
| Up | ||||||||||||||
| Down | ||||||||||||||
e) What value do the relative frequencies (rf) of each of the outcomes approach as the number of trials of the randomized experiment increases?
f) What could we say is, approximately, the probability of each of the events in this random experiment?
Observacions i context
- Maria Goeppert was born in Katowice, Upper Silesia, then part of Germany. She was the second woman in history to be awarded the Nobel Prize in Physics in 1963.
- Although at the age of 24 she already had a PhD in physics, and despite having studied quantum mechanics with teachers such as Max Born, James Franck and Adolf Windaus, she was not able to get a paid job at any university. She worked most of her life in different American universities, free of pay. "Volunteer", "intern" and "research associate" were some of the job titles that Maria Goeppert Mayer received over 30 years leading scientific investigations that would award her the Nobel Prize in Physics in 1963.
- She did research "just for the pleasure of doing physics", she wrote in her biography, published by the Nobel prize. She did not get a renowned and paid job until the age of 54, in 1960: a full-time position as a professor of physics at the University of California, in San Diego.
- At the same time as Maria, important mathematicians were developing their work, such as Hilda Geiringer (1893-1973) in statistics and probability; Mary Lucy Cartwright (1900-1998) in analysis; Olga Taussky Todd (1906-1995) in number theory and matrix theory; Marjorie Lee Brown 1914-1979) in linear and matrix algebra; Antonia Ferrín (1914-2009) in astronomy, 1914-2009; María J. Wonanburger Planells (1927-2014) in group theory and algebra; and Irène Joliot-Curie (1897-1956) in physics and chemistry.
- Among her predecessors, in the field of statistics and probability, we find Florence Nightingale (1820-1910), known for applying statistics to nursing and creator of sector diagrams. In the branch of physics, to which she dedicated herself, Marie Curie (1867-1934) was her predecessor. In mathematics and computer science, Ada Lovelace (1815-1852) stands out.
Descripció
In this activity we will work on the concept of probability of equiprobable events through a practical experiment that will be carried out by the students. We will calculate the probability empirically from the relative frequencies.