# DHS 18.1 - Option 18. Decisions Ryabushko AP

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# Description

Solve the following problems (1 - 6)

1.18. How many different five-digit numbers can be written using the digits 1, 2, 3, 4, 5, 6, 7, 8, 9 (without repetitions),?

2.18. On a shelf at random are placed 10 books. Determine the probability that this will be three specific books standing side by side.

3.18. Under certain specific conditions, the probability to bring down the enemy plane from the first anti-aircraft gun is equal to 0.4, from the second - 0.5. It made one shot. Find the probability that: a) the aircraft is destroyed in two rounds; b) aircraft struck at least one projectile; c) none of the projectile does not hit the target.

4.18. In the collector 16 parts produced at the plant number 1, and 10 parts produced at the plant number 2. The probability that the parts will survive the warranty period for parts with plant number 1 are equal to 0.8; factory number 2 - 0.9. a) Find the probability that the part will work to take the guesswork warranty period, b) take the guesswork worked part warranty period. At some of the plants it is likely to be made?

5.18. Products coming from a shop in the OTC does not satisfy the conditions of the standard in an average of 8% of cases. Find the probability that randomly taken from seven products do not satisfy the standard conditions: a) Six products; b) at least six articles; c) at least six articles.

6.18. The probability of occurrence of an event in each of 2000 independent tests is 0.7. Find the probability that the event occurs at least 1,500 times.