# DHS 18.1 - Option 13. Decisions Ryabushko AP

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Solve the following problems (1 - 6)

1.13. In how many ways you can create a patrol of three soldiers and an officer, if there is 80 soldiers and 3 officers?

2.13. From the party details, including 100 standard and 5 rejected, for the control of random taken 12 pcs. When checking it was found out that the first 10 of the 12 pieces - standard. Determine the probability that the next item will be the standard.

3.13. The probability that a student will pass the first exam, is 0.9 second - 0.7, the third - 0.6. Calculate the probability that a student will pass: a) two exams; b) at least two exams; c) no more than two exams.

4.13. In the event of normal operation the production line triggered alarm type T-1 with a probability of 0.9 and signaling type T-2 with a probability of 0.8. The likelihood that the line is provided with detectors of T-1 and T-2 are, respectively, 0.7 and 0.3. a) Find the probability that a deviation from the regular operation mode switch work, b) Warning load. What type he likely belong?

5.13. When stamping products is on average 20% of marriage. For control eight selected products. Find: a) the probability that the two products will be defective; b) the most probable number of defective products; c) the probability of the most probable number of defective products.

6.13. The equipment consists of 1000 items. The probability of failure of one element of the time T is 0.001 and does not depend on the operation of other elements. Failure probability to find at least two elements.