An example of solving problems in probability theory from the exam

Mathematics is a pretty versatile subject. Now we propose to consider an example of solving problems in probability theory, which is one of the areas of mathematics. We will immediately state that the ability to solve such tasks will be a big plus when passing the unified state exam. The tasks on the probability theory of the exam are in part B, which, respectively, is rated higher than the test tasks of group A.

Random events and their probability

It is this group that is being studied by this science. What is a random event? In any experiment, we get the result. There are tests that have a definite result with a probability of one hundred or zero percent. Such events are called reliable and impossible, respectively. We are interested in those that can happen or not, that is, random. To find the probability of an event, use the formula P = m / n, where m are the options that satisfy us, and n are all possible outcomes. Now consider an example of solving problems in probability theory.

Combinatorics. Tasks

Probability theory includes the next section, tasks of this type are often found on the exam. Condition: the student group consists of twenty-three people (ten men and thirteen girls). You need to choose two people. How many ways are there to choose two guys or girls? By condition, we need to find two girls or two men. We see that the wording tells us the right decision:

1. We find the number of ways to choose men.
2. Then the girls.
3. Add up the results.

We perform the first action: = 45. Next, the girls: and we get 78 ways. Last action: 45 + 78 = 123. It turns out that there are 123 ways to choose same-sex couples such as the headman and deputy, it does not matter girls or men.

Classical Tasks

We have considered an example from combinatorics, move on to the next stage. Let us consider an example of solving problems in probability theory for finding the classical probability of the origin of an event.

Condition: You have a box in front of you, inside there are balls of different colors, namely fifteen white, five red and ten black. You are offered to pull one at random. What is the probability that you will take the ball: 1) white; 2) red; 3) black.

Our advantage is the calculation of all possible options, in this example we have thirty of them. Now we have found n. Denote by A the extracted white ball, we get m equal to fifteen - these are successful outcomes. Using the basic rule for finding probability, we find: P = 15/30, i.e. 1/2. With such a probability we will come across a white ball.

In a similar way we find B - red balls and C - black. P (B) will be 1/6, and the probability of the event is C = 1/3. To check whether the problem is solved correctly, you can use the rule of sum of probabilities. Our complex consists of events A, B and C, in total they should be one. As a result of the check, we got the same desired value, which means that the task is solved correctly. Answer: 1) 0.5; 2) 0.17; 3) 0.33.

USE

Consider an example of solving problems in probability theory from USE tickets. Coin throwing examples are common. We offer to disassemble one of them. The coin is thrown three times, what is the probability that the eagle and the tails will fall twice. We reformulate the task: throw three coins at a time. To simplify the table. For one coin, everything is clear:

Two coins:

With two coins we already have four outcomes, but with three a little the task becomes more complicated, and there are eight outcomes.

Now we count the options that suit us: 2; 3; 4. We get that three out of eight options satisfy us, that is, the answer is 3/8.