IDZ 18.1 – Option 3. Solutions Ryabushko A.P.

Solve the following problems (1 – 6):

1.3. This course covers 12 disciplines, and every day 3 subjects are included in the class schedule. In how many ways can you create a class schedule for each day?

2.3. From a batch of bushings produced by a turner during a shift, 10 pieces are randomly selected for control. Find the probability that among the selected bushings two are of the second grade, if in the entire batch there are 25 bushings of the first class and 5 of the second.

3.3. The unit includes three radio tubes, the probability of failure of which during the warranty period is 0.3; 0.2; 0.4 respectively. What is the probability that during the warranty period the following will fail: a) at least two radio tubes; b) not a single radio tube; c) at least one radio tube?

4.3. Among the parts received for assembly, 30% are from plant No. 1, and the rest are from plant No. 2. The probability of defects for plant No. 1 is 0.02, for plant No. 2 – 0.03. Find: a) the probability that a part taken at random is standard; b) the probability of production at plant No. 1 of a randomly taken standard part.

5.3. Among the workpieces produced by workers, on average 4% do not meet the requirements of the standard. Find the probability that among 6 workpieces taken for control, the requirements of the standard do not meet: a) at least five; b) no more than five; c) two.

6.3. The probability of an event occurring in each of the independent trials is 0.2. Find the probability that the event will occur 25 times in 100 trials.

IDZ 18.1 – Option 3. Solutions Ryabushko A.P.

This product represents solutions to problems from Individual Homework (IH) in mathematical analysis 18.1, option 3, completed by A.P. Ryabushko.

The product contains detailed and understandable solutions to problems that will help students improve their knowledge in mathematical analysis and prepare for the exam.

The solutions are presented in a clear and understandable form, with all intermediate calculations and explanations provided.

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IDZ 18.1 – Option 3. Solutions Ryabushko A.P. is a product containing solutions to problems in mathematical analysis 18.1, option 3. The product contains solutions to six problems:

1.3. The problem is about the number of ways to create a class schedule for each day. Students study 12 disciplines, and every day 3 subjects are included in the class schedule. Solving the problem comes down to finding the number of combinations of 12 by 3, i.e. C(12,3) = 220.

2.3. The problem is about the probability of selecting 2 bushings of the second grade from a batch of bushings made during a shift by a turner. The entire batch contains 25 bushings of the first grade and 5 bushings of the second class. Solving the problem comes down to finding the number of combinations of 5 by 2 and 25 by 8, and then applying the conditional probability formula.

3.3. The problem of the probability of failure of radio tubes. The unit includes three radio tubes, and the probability of their failure is 0.3; 0.2; 0.4 respectively. Solving the problem comes down to finding the probabilities of the events “at least two radio tubes will fail,” “not a single radio tube will fail,” and “at least one radio tube will fail,” using Bernoulli’s formula.

4.3. Problem about the probability of defective parts. Among the parts received for assembly, 30% are from plant No. 1, and the rest are from plant No. 2. The probability of defects for plant No. 1 is 0.02, for plant No. 2 – 0.03. Solving the problem comes down to finding the probabilities of the events “the part is standard”, “the part was manufactured at plant No. 1 and turned out to be standard”, using the total probability formula and the conditional probability formula.

5.3. The problem of the probability of non-satisfaction of the standard requirements. Among the workpieces produced by workers, on average 4% do not meet the requirements of the standard. It is necessary to find the probability that among 6 workpieces taken for control, the requirements of the standard will not be satisfied: no less than five, no more than five, two. The solution to the problem is based on the application of Bernoulli's formula.

6.3. The problem of the probability of an event occurring in independent trials. The probability of an event occurring in each of the independent trials is 0.2. You need to find the probability that an event will occur 25 times in 100 trials. The solution to the problem is based on the application of Bernoulli's formula.

The solutions to the problems presented in the product by Ryabushko A.P. seem correct and are based on appropriate mathematical formulas and methods. However, I cannot guarantee the complete correctness of the decisions without more detailed analysis and verification. If you have any questions or doubts about the solutions, it is recommended that you seek assistance from qualified teachers or experts in the relevant field of mathematics.

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IDZ 18.1 – Option 3. Solutions Ryabushko A.P. is a set of solutions to six problems in mathematical statistics and probability theory.

The first task is to determine the number of ways to create a class schedule if each day includes three subjects, and 12 disciplines are studied in the general program.

The second task is associated with determining the probability that from a sample of 10 bushings selected at random from a batch containing 25 bushings of the first grade and 5 bushings of the second class, two will be of the second class.

The third task requires determining the probability that of three radio tubes with a probability of failure of 0.3; 0.2 and 0.4, at least two will fail during the warranty period, none will fail and at least one will fail.

The fourth problem involves determining the probability that a randomly selected part turns out to be standard if 30% of all parts are produced at plant No. 1, for which the probability of defects is 0.02, and the remaining parts are produced at plant No. 2, for which the probability of defects is 0. ,03. Also in this problem you need to determine the probability that a randomly selected standard part is produced at plant No. 1.

The fifth task is to determine the probability that from a sample of 6 workpieces produced by a worker, at least five will not satisfy the standard, no more than five will not satisfy the standard, and exactly two will not satisfy the standard, if for each workpiece the probability of not meeting the standard is 4% .

The sixth problem requires determining the probability that in a series of 100 independent trials, in each of which the probability of an event occurring is 0.2, the event will occur exactly 25 times.

Solutions to problems are prepared in Microsoft Word 2003 using the formula editor.

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