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.

Detailed solution. Designed in PDF format for easy viewing of IDZ solutions on smartphones and PCs. In MS Word (doc format) sent additionally.