27/06/2018

Mega-Sena illustrates the mysteries of chance.

Reproduction of Marcelo Viana's column in Folha de S. Paulo.

Of all areas of mathematics, probability is the one that most challenges our intuition. How can the science of exactness deal with uncertainty?

The first advances motivated by games of chance date back to the 16th and 17th centuries, but the theory only became consolidated in the 20th century, with the work of the great Soviet mathematician Andrey Kolmogorov (1903-1987).

The mathematics of probability is based on the fact that, even when the outcome is uncertain, many interesting things can be said if the experiment is repeated many times.

When we flip a coin, there's no way to know which side it will land on. But you can be sure that if you do it a thousand times or more, there will be at least 49% heads and 49% tails.

All this comes about because of this week's peculiar Mega-Sena result: all six winning numbers begin with the digit 5. But is that as surprising as it seems?

There are 50,063,860 possible combinations in the Mega-Sena lottery, and all are equally likely: the chance of getting 50, 51, 56, 57, 58, 59, as happened, is exactly the same as any "unpleasant" combination.

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