Mathematics is one of the most difficult subjects among school subjects. And everything would be fine if it were not for him to take it in the eleventh grade, and even in the form of an exam. Not only that, part A was removed from this exam a few years ago, in which it was only necessary to choose the correct answer from the several proposed ones, so also the probability theory was added to the school curriculum, and therefore to the test tasks.
Fortunately, so far there is only one such task, but it still needs to be solved. As a rule, graduates at the exam are worried, and knowledge of how to calculate the probability of an event completely flies out of their heads. To avoid this, it is necessary to learn this material well at the stage of preparation for the exam.
So what is the probability of an event? This concept has several definitions. Most often considered the so-called "classic". The probability of an event occurring is the ratio of the number of favorable outcomes to the number of all possible ones: P = m / n.
The following properties follow from this definition:
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 range from zero to unity.
But knowledge of the definition and properties is often not enough to solve the task on this topic
at the Unified State Exam. The probability of an event sometimes needs to be calculated using addition and multiplication theorems. Which one to apply depends on the conditions of the problem. Here everything is somewhat more complicated, but if you want and zeal to master this material is quite possible.
If two events cannot simultaneously appear as a result of one test, then 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 (multiplication theorem). Such can be, for example, hitting the target during firing from two guns. In other words, independent events are those whose outcomes are independent of each other.
If the test results are interconnected, then conditional probability is used. Such events are called dependent.
To calculate the probability of one of them, you must first calculate what it is equal to the other. So, first of all, they determine which event entails another. Then calculate its probability. Assuming that this event has occurred, they find the same value for the second. The conditional probability in this case is calculated as the product of the first number obtained by the second. If there are several such events, then the formula becomes more complicated, but we will not consider it, since at the USE this will not be useful to us.
Any topic can be easily learned if you get a good understanding of the subject matter. The probability of an event is no exception. To easily solve any problems from this section of mathematics, you need to be able to think logically and know the corresponding definitions and formulas that are described above. Then you are not afraid of any exam!