By: Zoe Fouka – 3rd General Lyceum of KarditsaAntónıo Nozes - Escola Secundárıa com 3 Cıclo D. Manuel I

Laplace

Pierre Simon Laplace (1749 – 1827) was born at Beaumont-en-Auge in Normandy. He was a French mathematician, philosopher and astronomer. Because of his great mathematical potential, Laplace went to Paris at the age of 19, where he started his career. There, he began submitting mathematical papers, in order to get into the Science Academy in Paris. Some of his papers were about the theory of probability and statistics.

According to Laplace, in probability theory we give the probabilities of some simple events and then, we try to determine the probabilities of compound events. Laplace called the probabilities of the simple events, possibilities.

The theory of probability

Example – The launch of a coin

We can try to throw a coin.

The possible results are:

How can we know if we will get face or crown?

Face Crown

Getting face or crown depends on the "chance" of "luck" or "unluck" ...

The behaviour before throwing the coin can not determine which one of the results will come out.

We are in the presence of a "random phenomenon ", wich in probabilities is called a "random experiment".

Weel of Fortune

Rules: The player ( Mr. Thomas) wins the contest if he gets one of the two red parts.

What is the probability of Mr. Thomas to win the contest?

There are 8 sectors on the wheel and only two are red. So, there are eight possible cases.

There are two "favorable cases" marked with red, so we can say that the chance of 'getting red' is 2 to 8, this is, 2 / 8.

We can say that:

P(“getting red”)=the probability of an event comes in the form of fraction and it should be simplified whenever is possible.

So, the probability of Mr. Thomas winning is 1/4

One well-known formula is the rule of succession, which was introduced by Laplace in order to solve the sunrise problem:

"What is the probability that the sun will rise tomorrow?

Suppose that we conduct an experiment and we know that its result will be a "success" or a "failure". If we repeat this experiment over and over again, for n times and get s successes, then what is the probability that the next repetition will be a success again?

P(next outcome is a success) = s + 1/ n + 2

Laplace calculated the probability that the sun will rise tomorrow, given that it has never failed to in the past. (d is the number of times the sun has risen in the past)

P(sun will rise tomorrow) = d+1/ d+2

The Rule of Succession

The End