DHS 18.1 - Option 6. Decisions Ryabushko AP

Solve the following problems (1 - 6)

1.6. At a conference of the three groups of students choose one specialty one delegate. It is known that in the first group 25, the second - in the third 28 and - 20. Determine the number of possible delegations, if you know that every student from any group with equal probability can be a part of the delegation.

2.6. I made up the word "repair" of the letters of the alphabet split. Cards with individual letters are thoroughly mixed, then randomly pull 4 cards and lay them in the extraction procedure. What is the probability of getting at the same time the word "sea"?

3.6. When one cycle of the review of three radar stations, watching the spacecraft, its probability of detection equal to 0.7, respectively; 0.8; 0.9. Find the probability that the survey ship one cycle: a) three stations is detected; b) is detected by at least two stations; c) not be detected.

4.6. The preform can proceed to process one of the two machines with the probabilities of 0.4 and 0.6 respectively. In the processing in the first machine defect probability is 2%, the second - 3%. Find the probability that: a) randomly taken after processing the product - standard; b) randomly taken after treatment with standard product processed on the first machine.

5.6. The probability of each of the seven motors currently equals 0.8. Find the probability that at the moment includes: a) at least one motor; b) The two engines; c) three motors.

6.6. The probability of occurrence of an event in each of the independent trials is 0.2. Find the probability that the event occurs 20 times in 100 trials.