# DHS 18.1 - Option 15. Decisions Ryabushko AP

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Solve the following problems (1 - 6)

1.15. In how many different ways you can choose from the 15 people delegation of three people?

2.15. Literal lock comprises 5 to sheathe the axis drives, each of which is divided into 6 sectors with different letters deposited thereon. The lock can only be opened if each disc occupies a certain position relative to the lock housing. Determine the probability of opening of the lock, if installed an arbitrary combination of letters.

3.15. Two bomber overcome air defense zone. The probability that the first bomber is shot down, equal to 0.7, the second - 0.8. Find the probability of: a) destruction of the bomber; b) the destruction of the two bombers; c) errors.

4.15. In the coming assembly parts with three conveyors. First give 25%, the second - third 30 - 45% of the parts entering the assembly. From the first line in an average of 2% comes marriage, the second - 3, in the third - 1%. Find the probability that: a) the assembly received a defective item; b) delivered to the assembly defective part - from the second conveyor.

5.15. Wholesale base serves 6 stores. The probability of receiving an application base on a given day for each of the stores is 0.6. Find the probability that this day will be: a) five applications; b) at least five requests; c) not more than five applications.

6.15. The machine consists of 2,000 independently operating units. The probability of failure of one unit during the year is equal to 0.0005. Find the probability of failure for a year of two nodes.