# DHS 18.1 - Option 29. Decisions Ryabushko AP

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Solve the following problems (1 - 6)

1.29. The CD has 10 telephone numbers. Each has a PBX phone number recorded by a five-digit number, and they have the first figure is the same. Find the greatest possible number of subscribers of this station, whose last 4 digits of the telephone number is different.

2.29. The party, consisting of 20 radios, 5 faulty. Randomly take 3 radio. What is the probability that the number selected will include 1 and 2 faulty serviceable radio?

3.29. Engineer calculates, using three directories. The probabilities that the data are of interest to him in the first, second, third, reference books, are, respectively, 0.6; 0.7; 0.8. Find the probability that the data of interest to the engineer contains: a) only in one directory; b) only two references; c) in all three references.

4.29. At the assembly parts come with four machines. It handles 40% of the first, second - 30, the third - fourth and 20 - 10% of all items entering the assembly. The first machine gives 0.1% of marriage, the second - 0.2, the third - 0.25, the fourth - 0.5%. Find the probability that a) the assembly will come standard item; b) received on a standard assembly member is made the first machine.

5.29. Among the parts manufactured by working, an average of 4% defective. Find the probability that among control made at five parts: a) two defective; b) at least one defective; c) no more than one defective.

6.29. The average density of pathogenic bacteria in 1 m3 of air is equal to 100. take the sample 2 dm3 air. Find the probability that at least one bacterium is found therein.