The problem of the three doors
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
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.
Talking about probabilities, do you know the problem of the three doors? It is a mathematical problem of probability that is inspired by a television game show.
The problem is as follows: the contestants have to choose a door among three that are closed and the prize is to take what is behind the chosen door. It is known for sure that one of the doors hides a car, while behind the other two there is a goat. Once the contestants have chosen a door, they communicate it to the public and the presenter. The latter opens one of the two doors that have not been chosen and shows that behind it there is a goat. At that time, the option to change the door is given to the contestants. Should the contestants keep their original choice or choose another door? Is there any difference?
Analyse the problem posed and find, in a reasoned way, the best possible solution for the contestants.
Observations and 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.
Description
In this activity we will work on the concept of conditional probability and how to obtain additional probabilistic information through an example, with the mythical Monty Hall problem, based on a television game show.