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# Probability theory

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# Description

1. In a trading company received three TV manufacturing companies in the ratio of 2: 5: 3. TV coming from the first company, in need of repair during the warranty period, in 15% of cases of the second and third - respectively 8% and 6% of cases. Find the probability that received by the trading firm TV need repair during the warranty period.

2. Dana function F =

Find the variance.

3. Investment Analyst collects data about the actions and notes whether paid dividends on them or not, and increased share price for the period of interest to him. The data collected are presented in the following table:

Dividends increased price has not increased Total Price

Produce

Not to produce 51

97 83

72134

169

Total 148 155 303

Knowing that the event has grown and grown the probability that the price increase is equal to price. Find the probability that it also paid dividends.

4. textbook published edition 90 000 copies. The likelihood that the textbook is defective 0.00008. Find the probability that at least 9998 books stitched correctly.

5. subscription service delivered 5 TVs. It is known that the expected number of failures in a year for five television is one. If TVs have the same probability of failure-free operation, what is the probability that the year will require at least one repair?

# Additional information

6. To study the efficiency of a particular breed of poultry measure the diameter of the eggs. The greatest transverse diameter of the eggs is a random variable distributed according to a normal distribution with a mean of 5 cm and a standard deviation of 0.3 cm. Find the probability that the diameter of the eggs taken at random will be concluded in the range from 4.7 to 6.2 cm.

7. Of the 10 variants of the control work, written on separate cards, randomly selected and distributed eight eight students, seated on the same row. Find the probability that the embodiments 1 and 2 will be unused.

8. The stack 20 of punched cards marked numbers 101, 102, ..., 120 and arbitrarily positioned. Randomly selected three cards. Find the probability that the card is removed from №101.

9. The farm has 100 cars. Probability of failure of each of them over a period of 0.9. Rate the likelihood that the deviation of the number are excellent vehicles for a certain period of its expected value does not exceed modulo 5.

10. The eight-volume collection of works placed on the shelf at random. Find the probability that the volume with number 1 and number 2 will be in one volume.

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