Mathematics - one of the most difficult subjects among school subjects.And all would be nothing if it did not have to pass in the eleventh grade, and even in the form of the exam.Not only is this test a few years ago removed a part A, which had only to choose the right answer from a few sentences so also probability theory added to the school curriculum, and hence in job tests.
Fortunately, this problem is only one, but face it you still need.As a rule, graduates of the exam are worried, and knowledge of how to calculate the probability of an event, they fly completely out of my head.To avoid this, you should be good to learn the material at the stage of preparation for the exam.
So, what is the probability of the event?There are several definitions of the concept.Most often considered the so-called "classical".The probability of occurrence of the event - is the ratio of favorable outcomes to the number it all possible: P = m / n.
This definition implies the following properties:
1. If an event is certain, its probability is equal to unity.In this case, all outcomes are favorable.
2. If the event is not possible, then its probability is zero.This case is characterized by the absence of a favorable outcome.
3. The value of the probability of any random event lies in the interval from zero to one.
But knowledge of the definition and properties are often not sufficient to solve the task on this topic at a unified state exam.The probability of events sometimes need to calculate by means of the theorems of addition and multiplication.Which one to use depends on the conditions of the problem.Here, everything is more complicated, but if you wish and diligence to learn the material is possible.
If two events can not both be the result of one test, they called inconsistent.Their probability is calculated by the addition theorem:
P (A + B) = P (A) + P (B), where A and B - incompatible events.
probability of independent events is calculated as the product of the corresponding values for each of them (multiplication theorem).These may be, for example, hitting the target while firing two guns.In other words, independent events - those outcomes which are independent of each other.
If the test results are interrelated, then use the conditional probability.The events are called dependent.
To calculate the probability of one of them, you must first consider what it is for another.Thus, in the first place, it is determined what event entails more.Then calculate its probability.Assuming that the event occurred, are the same value for the second.Conditional probability in this case is calculated as the product of the first number by the latter.If several of these events, the formula is complicated, but we will not be considered, because the exam is not useful to us.
any topic you can easily learn, if it is good to understand the essence of the issue.The probability of the event - is no exception.To solve any problems of this branch of mathematics, we must be able to think logically and know the relevant definitions and formulas described above.Then no exam you not afraid!