Mathematics is one of the most difficult subjects in school. And everything would be fine if it were not necessary to take it in the eleventh grade, and even in the form of the exam. Not only was Part A removed from this exam a few years ago, in which you only had to choose the correct answer from several proposed ones, but also the theory of probability was added to the school curriculum, and therefore to the test tasks.
Fortunately, there is only one such problem so far, but it still needs to be solved. As a rule, graduates are worried during the exam, and the knowledge of how to calculate the probability of an event completely flies out of their heads. To prevent this from happening, it is necessary to master this material well even at the stage of preparation for the exam.
So, what is the probability of an event? This concept has several definitions. Most often, the so-called "classic" is considered. The probability of an event occurring isthe ratio of the number of favorable outcomes to the number of all possible outcomes: Р=m/n.
The following properties follow from this definition:
1. If an event is certain, its probability is equal to one. In this case, all outcomes will be favorable.
2. If an event is impossible, then its probability is zero. This case is characterized by the absence of favorable outcomes.
3. The probability value of any random event lies between zero and one.
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 use depends on the condition of the problem. Here everything is somewhat more complicated, but with the desire and diligence, it is quite possible to master this material.
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 values for each of them (multiplication theorem). These can be, for example, hits on 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 interrelated, then useconditional probability. Such events are called dependent.
To calculate the probability of one of them, you must first calculate what it is equal to for the other. So, first of all, it is determined which event entails another. Then its probability is calculated. Assuming that this event has occurred, 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 it will not be useful to us at the USE.
Any topic can be easily learned if you get to the heart of the matter well. 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 relevant definitions and formulas that are described above. Then no exam is scary for you!
