Mathematical probability. Its types, how the probability is measured

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Mathematical probability. Its types, how the probability is measured
Mathematical probability. Its types, how the probability is measured
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Probability is a way of expressing the knowledge or belief that an event will happen or has already happened. The concept has been given a precise mathematical meaning in a theory that is widely used in research areas such as mathematics, statistics, finance, gambling, science, and philosophy to draw conclusions about the possibility of potential events and the underlying mechanics of complex systems. The word "probability" has no agreed direct definition. In fact, there are two broad categories of interpretations, whose adherents have different views on its fundamental nature. In this article you will find a lot of useful things for yourself, discover mathematical concepts, find out how probability is measured and what it is.

Probability types

What is it measured in?

There are four types, each with its own limitations. None of these approaches are wrong, but some are more useful or more general than others.

Probability formulas
  1. Classical probability. Thisthe interpretation owes its name to the early and August genealogy. Advocated by Laplace and found even in the work of Pascal, Bernoulli, Huygens, and Leibniz, it assigns probability in the absence of any evidence or in the presence of symmetrically balanced evidence. The classical theory applies to equally probable events, such as the outcome of a coin or dice toss. Such events were known as equipossible. Probability=number of favorable equipossibilies/total number of appropriate equipossibilities.
  2. Logical probability. Logical theories retain the idea of ​​the classical interpretation that they can be determined a priori by exploring the space of possibilities.
  3. Subjective probability. Which is derived from a person's personal judgment about whether a particular outcome can occur. It contains no formal calculations and reflects opinions only

Some of the probability examples

In what units is the probability measured:

Probability Example
  • X says, "Don't buy avocados here. They're rotten about half the time." X expresses his belief about the likelihood of the event - that the avocado will be rotten - based on his personal experience.
  • Y says: "I'm 95% sure the capital of Spain is Barcelona." Here, Y's belief expresses the probability from his point of view, because only he does not know that the capital of Spain is Madrid (in our opinion, the probability is 100%). However, we can consider it as subjective, since it expressesmeasure of uncertainty. It's like Y saying, "95% of the time I feel as confident as I do this, I'm right."
  • Z says, "You're less likely to get shot in Omaha than in Detroit." Z expresses a belief based (presumably) on statistics.

Math processing

How is probability measured in mathematics?

How is probability measured?

In mathematics, the probability of an event A is represented by a real number in the range from 0 to 1 and is written as P (A), p (A) or Pr (A). An impossible event has a chance of 0, and a certain one has a chance of 1. However, this is not always true: the probability of a 0 event is impossible, just like 1. The opposite or complement of an event A is an event not A (that is, an event A that does not occur). Its probability is determined by P (not A)=1 - P (A). As an example, the chance of not rolling a six on a hex die is 1 – (the chance of rolling a six). If both events A and B occur on the same run of the experiment, this is called an intersection, or the joint probability of A and B. For example, if two coins are turned over, there is a chance that both will come up heads. If event A, or B, or both occur in the same execution of the experiment, this is called the union of events A and B. If two events are mutually exclusive, then the probability of their occurrence is equal.

Hopefully now we have answered the question of how probability is measured.

Conclusion

The revolutionary discovery of 20th century physics was the random nature of allphysical processes occurring on a subatomic scale and subject to the laws of quantum mechanics. The wave function itself evolves deterministically as long as no observations are made. But, according to the prevailing Copenhagen interpretation, the randomness caused by the collapse of the wave function on observation is fundamental. This means that the theory of probability is necessary to describe nature. Others have never come to terms with the loss of determinism. Albert Einstein famously remarked in a letter to Max Born: "I am convinced that God does not play dice." Although there are alternative points of view, such as quantum decoherence, which is the cause of the seemingly random collapse. There is now strong agreement among physicists that probability theory is necessary to describe quantum phenomena.

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