Why is the probability between 0 and 1

probability

Every day we come across statements about the probability of events. The probability that another bank will go bust is 41.4%. The US bank Morgan Stanley sees a 40% probability that the Federal Constitutional Court will grant the urgent motions against the ESM. Martin assumes that he has a 50% chance of answering the yes-no question correctly. All of these are examples of probabilities that we come into contact with on a daily basis.

When we calculate probabilities, we give their value with a number between 0 and 1. Percentages between 0 and 100% correspond to this value between 0 and 1.

definition

Probability assigns a numerical value between 0 and 1 to the occurrence of an event. The closer the probability is to the number 1, the sooner the event will occur.

  • If the probability is equal to 1, the event is guaranteed to occur. One speaks of one safe event.
  • If the probability is 0, the event will not occur. One speaks of one impossible event.

In mathematics, information about the probability of an event is given using the notation P (A) = 0.1, where P stands for the English word for probability (probability), A is the event whose probability is being calculated and the value after the equal sign (in this case 0.1) is the numerical value for the occurrence of A.

It is important to know what assigning a probability to an event means, as we do this quite often in everyday life without spending much time on the actual calculation. Also and precisely because of this:

  1. The intuitive assignment of a probability to an event requires a certain experience or opinion of how the future might behave.
  2. The probability can also be calculated using the relative frequency. The relative frequency indicates how often a favorable event for us occurs in a total of events. Here is an example: There are 20 students in a school class, 11 of them are girls, the remaining 9 are boys. The odds that a randomly chosen student will be a girl are:

  3. If the probability of the results occurring is the same, the probability can be calculated using Laplace's formula:

Brief history of probability

The basic concepts and ideas of probability theory existed hundreds of years ago, but probability theory and statistics were not recognized as a separate branch of mathematics until the mid-17th century. In France at the time, gambling was widespread as it was not forbidden by law. The more complicated the game, the higher the chances of winning. This gave rise to the need to use mathematical methods to precisely calculate the chances of victory or defeat.

The real hour of birth of the calculus of probability begins, however, when the nobleman Blaise Pascal asked for the answer to the birth problem as we know it today. A friend of Pascal's, Chevalier de Méré, often gambled to make money. He bets that if he rolls the dice four times in a row, at least one of the rolls will be a 6. He knew from experience that this worked more often than not. To make the game more interesting, he changed rules. Now he had to throw two dice 24 times, whereby in at least one of the throws both throws had to have a 6 for him to win. He quickly realized that he was making less money with this method than before. He asked his friend Pascal why this was so. He calculated that the probability of winning with the new rules of the game was 49.1%, while with the old rules of the game it was 51.8%.

According to tradition, the question as formulated by Chevalier de Méré is said to have established a correspondence between Blaise Pascal and the French mathematician Pierre de Fermat. Historians believe that the first letters between the two dealt with the dice problem and other probabilistic questions. Therefore, Blaise Pascal and Pierre de Fermat are considered to be the founders of the calculus of probability.

Nowadays, probability is no longer limited to just gambling. Especially in insurance, commercial quality assurance, quantum mechanics, genetics and many other areas, probability theory and statistics play a decisive role.