Mathematics for critical thinking
How does the choice of voting system influence the outcome of an election?
In France, we are used to two-round elections. However, there are other voting systems used in different countries or devised by mathematicians. With the same distribution of votes, each system leads to the election of a different person... Will democracy remain a mathematical puzzle?
Find out more: Mr. President, did you really win this election? - Statistics explained to my cat
How can you interpret the results of a study or survey without making a mistake?
We are used to reading polls in absolute terms: 49% yes, 51% no! In reality, the results of polls and scientific studies are obtained from a sample of the population and therefore have a margin of error. Mathematical statistics allow us to specify this margin, called the confidence interval, which narrows as the sample size increases, but which should above all be included in all publications of poll results.
Find out more: CCNMO - Understanding a confidence interval
It is not enough to know how to calculate; one must also know how to interpret the data.
Simpson's statistical paradox is highly counterintuitive: it is possible for a phenomenon to occur within different groups, but for this phenomenon to be reversed when the groups are combined. How can we know what conclusions to draw and make the right decisions?
Find out more: Simpson's paradox illustrated by Covid-19 vaccination data and Can we rely on the figures? (Elise Janvresse - VideoDiMath)
Why does a positive test not always mean you are sick?
A well-known psychological phenomenon often leads us to confuse what are known as conditional probabilities. For example, the probability of being sick when our test for a disease is positive with the probability that the test will be positive when we are sick. Bayes' theorem allows us to link these two probabilities, which can be very different.
Find out more: Conditional Probabilities - France Bleu
Probabilities: the secret tool for winning the lottery?
Can you win the lottery by playing the numbers 1, 2, 3, 4, 5, 6? Well, yes! You have about a 1 in 19 million chance of this combination being drawn... Just like any other combination. However, there are certain strategies that can (perhaps) maximize your winnings! For example, you can choose numbers that others are less likely to choose so that you don't have to share your winnings if you win.
Find out more: Can you win the lottery by checking the numbers 1, 2, 3, 4, 5, 6? - RadioFrance
Are there laws of chance?
When you flip a coin, the result is of course unpredictable. However, probability theory allows for the rigorous study of chance and the prediction of results over a large number of coin tosses. Galton's board provides a concrete illustration of certain theorems such as the law of large numbers and the central limit theorem.
Find out more: Galton's board - Salem Wizards
Is mathematics really the domain of certainty?
We often think that a mathematical result is either true and provable, or false. It's not that simple: Gödel's theorem states that there are “undecidable” propositions that cannot be proven or disproven.
Find out more: Gödel's theorem | Journeys to the land of maths | ARTE