# DHS 18.1 - Option 4. Decisions Ryabushko AP

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Solve the following problems (1 - 6)

1.4. Eight people have agreed to travel in the same train, consisting of eight cars. In how many ways you can distribute these people on cars, if each car sits on one person?

2.4. The six-storey building elevator on the ground floor includes 3 people. Each of these are equally likely to be released on any of the floors from the second. Find the probability that all the passengers will be released on the fourth floor.

3.4. In the first box 20 pieces, 15 of them - the standard in the second box of 30 pieces, 25 of them - a standard. From each box randomly take one piece. What is the probability that: a) both of the details will be standard; b) at least one item is the standard; c) both of the details non-standard?

4.4. Three machine parts are made of the same type, which are applied to the common pipeline. Performance of the first, second and third machines are correlated as a 2: 3: 5. The probability that the first item with the machine - the higher the quality, equal to 0.8, with the second - 0.6, with the third - 0.7. Find the probability that: a) taken at random from the conveyor will detail the highest quality; b) randomly taken higher quality item made the first machine.

5.4. The probability of winning three percent per one bond loan is 0.25. Find the probability that eight of winning purchased bonds will: a) three; b) two; c) at least two.

6.4. The probability of occurrence of an event in each of the 2,100 independent trials is 0.7. Find the probability that the event occurs at least 1,470 times and no more than 1500 times.