# DHS 18.1 - Option 12. Decisions Ryabushko AP

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Solve the following problems (1 - 6)

1.12. How many straight lines can be drawn through 8 points, if you know that any three of them lie on the same line?

2.12. In the group of six athletes from 8 sports masters. Find the probability that two randomly selected athletes at least one - the master of sports.

3.12. In the area of cross-country for motorbike riders, there are three obstacles. The probability of successful passage of the first obstacles is 0.4 second - 0.5, the third - 0.6. Find the probability of successful overcoming of: a) three obstacles; b) at least two obstacles; c) two obstacles.

4.12. Resistor supplied in television, may belong to one of the two parties with probabilities of 0.6 and 0.4. The probabilities that the resistor will work guarantee the number of hours for these parties are, respectively, 0.8 and 0.7. a) Find the probability that the resistor is taken at random will work guarantee the number of hours, b) Resistor guarantee the number of hours worked. To which party he likely belong?

5.12. The germination of seeds of lemon is 80%. Find the probability that the sown seeds of 9 rises: a) seven; b) not more than seven; c) more than seven.

6.12. Find the probability of simultaneous stopping 30 cars of 100 employees, it is unlikely to stop every car is 0.2.