DHS 18.1 - Option 25. Decisions Ryabushko AP

Solve the following problems (1 - 6)

1.25. The convoy, consisting of 30 cars, should allocate harvesting in farms 12 trucks. In how many ways can this be done?

2.25. The two men agreed to meet at a certain place between two and three o´clock in the afternoon. The visitor is waiting for another first for 10 minutes and then leave. What is the probability of meeting these people, if the arrival of each of them within the hour may occur at any time?

3.25. two independently working alarm set for alarm. The probability that the accident triggered the first indicator is equal to 0.9, the second - 0.7. Find the probability that an accident: a) both the alarm will work; b) does not work any alarm; c) work at least one signaling device.

4.25. Assembly parts come from three machines and with first 30%, the second 40 and third 30% of all components. The likelihood of marriage for the first machine is equal to 0.02, for the second - 0.03, for the third - 0.04. a) Find the probability that take the guesswork detail - defective b) take the guesswork item was defective. With a machine, it likely came?

5.25. The probability of a torpedo to sink the vessel is 0.2. Issued 5 torpedoes. Find the probability that there is: a) entering the three vessel; b) at least three hits; c) four hits.

6.25. The average number of calls received at the switch for 1 min is 2. Find the probability that in 6 minutes will go at least three call if the call flow assumes the simplest.