Probability theory and mathematical statistics RFEI

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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.

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