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# Probability theory and mathematical statistics RFEI

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Content: Теория вероятностей и мат статистика.rar (568,97 kB)

# Description

EXAMINATION QUESTIONS

On a subject

"Theory of Probability and Mathematical Statistics"

1. Who is the author of the mathematicians axiomatic theory

Probability?

2. The shopping the supermarket shelf are 5 different blocks

colors. What color combinations are possible to make,

If cubes spread in a line?

3. How many permutations of the letters of the word "business" in

which the letter "b" in the first place, and the letter "c" - at the end of words?

4. The shopping the supermarket shelf are 10 boxes of chocolates.

Of these, 3 boxes of caramel, 7 boxes of chocolates.

What is the probability of randomly take off the shelf a box of chocolate

candy?

5. What three-letter "words" can be formed from the letters of the word

"Account"? A word is any sequence of letters.

6. What events are called impossible?

7. In the company of 12 employees. For the formation of a corporate

the culture of the company should elect three critical - for

athletic performance for mass cultural and socio-

household. In how many ways this can be done?

8. Dice thrown once. What is the probability

that on the top of an odd number of points will fall?

9. What can not be equal to the probability of a

developments?

10. What events are called reliable?

11. What is the probability of getting an even number of toss

dice?

12. dice thrown once. What is the probability that

on the upper face fall the number of points, equal to 7?

13. In the package are 7 white and 3 green towels. Simultaneously

2 towels removed. What is the probability that both

lessons will be white towel? (Answer rounded to

to two decimal places).

14. A discrete random variable X has the distribution law

probably wondering table:

What is the expectation of M (X) is discrete

random variable X?

7

15. Find the expected number of defective products

batch of 10 000 units, if each product can be

defective with a probability of 0.005?

16. What is the variance of a random variable if its first value x1 - = 2

17. The shooter shoots at the target twice. The probability of falling into

Target 0.7. What is the probability that at least one shooter

just hit the target?

18. two hundred respondents were asked: "Do you higher

Education? "Eighty-four people responded

positively. What is the relative frequency of positive

response in this experiment?

19. Of the 100 sets of dishes made production

The company has 7 sets with defects. What is the

the probability that randomly selected 4 sets will be

without defects. (Answer rounded to the nearest tenth).

20. The shopping the supermarket shelf are 20 packs

butter. Of these, 13 packs of chocolate cream

oil, 7 packs of butter "Peasant". What is the

probability of randomly take off the shelf a pack of butter

"Country"?

# Additional information

21. The shop is open 7 men and three women. As Scheduled

numbers randomly selected three people. Find the probability that

that all men will be selected persons. (Answer rounded to

the nearest tenth).

22. The apparatus consists of two elements operating independently.

Probability of failure of these elements (for

working day) are, respectively, 75.0 and 9.0. What is the

the likelihood that during working hours, both will fail

element? (Answer given to three decimal places).

23. Among the 20 refrigerators delivered to the shop floor trading

central warehouse, 5 have a scratch on the side panel. What is the

the probability that two randomly selected among

refrigerators, both will have scratches on the side panel.

24. A discrete random variable X has the distribution law

Probability:

Find the expectation) X (M discrete random

the value of X.

25. Find the variance of a discrete random variable X, given

distribution law:

26. The bookstore is commercially available 8 types of directories

for entering universities, five of which - in a binder.

Seller took two random directory. Find the probability that

Both combined directory will be bound.

27. Two arrow shot at a target. The probability of falling into

target in one shot the first arrow is 0.6, and for

second - 0.7. Find the probability that at one salvo in

Target will get the two arrow.

28. The probability that a randomly taken from the warehouse seller

shopping center chair chairs from some parties, will

defective is 0.3. Find the probability that four

29. The two furniture factory supply warehouse shopping center

office furniture. Then the furniture is in no particular order

an exhibition hall in the shopping center. The probability that the

first furniture factory standard, equal to 0.7, and the second - 0.9.

Find the probability that at random taken office furniture -

standard.

30. Find the expected number of defective cars

1000 cars are on the Kursk station, if each car

It may be defective with probability 0.03.