What is the probability of an event? Helping students in the preparation for the USE

Mathematics is one of the most difficult subjects among school disciplines. And all would be nothing, if it was not necessary to hand over it in the eleventh grade, and even in the form of the Unified State Exam. Not only that part of this exam was deleted a few years ago from part A, in which it was only necessary to choose the correct answer from several of the proposed ones, so the theory of probabilities was added to the school program, and hence to the tests.

Fortunately, while this task is only one, but it still needs to be solved. As a rule, graduates in the exam are worried, and knowledge about how to calculate the probability of an event, completely fly out of their heads. To prevent this from happening, it is necessary to master this material well at the stage of preparation for the USE.

So, what is the probability of an event? This concept has several definitions. Most often they consider the so-called "classical". The probability of occurrence of an event is the ratio of the number of outcomes favorable to it to the number of all possible: P = m / n.

This definition implies the following properties:

1. If the event is reliable, its probability is one. In this case, all outcomes will be favorable.

2. If the event is impossible, then its probability is zero. This case is characterized by a lack of favorable outcomes.

3. The probability value of any random event lies in the interval from zero to one.

But knowledge of definition and properties is often not enough to solve the task on this topic at the Unified State Exam. The probability of an event can sometimes be calculated by means of addition and multiplication theorems. Which of them apply depends on the condition of the problem. Here everything is somewhat more complicated, but if you want and diligence to learn this material is quite possible.

If two events can not appear simultaneously as a result of one test, they are called incompatible. Their probability is calculated by the addition theorem:

P (A + B) = P (A) + P (B), where A and B are incompatible events.

The probability of independent events is calculated as the product of the corresponding quantities for each of them (the multiplication theorem). These can be, for example, hit the target while firing two guns. In other words, independent events are those whose outcomes do not depend on each other.

If the test results are interrelated, then the conditional probability is used. Events are called addicts.

To calculate the probability of one of them, you must first calculate what it is equal to the other. So, first of all, determine what event entails another. Then calculate its probability. Assuming that this event has come, find the same value for the second. The conditional probability in this case is calculated as the product of the first received number by the second. If there are several such events, then the formula becomes more complicated, but we will not consider it, since we will not need this on the USE.

Any topic can be easily learned, if you understand the essence of the matter. The probability of an event is no exception. To easily solve any problems from this section of mathematics, one must be able to think logically and know the corresponding definitions and formulas that are described above. Then no examination is terrible for you!