Solve the following problems (1 - 6)
1.21. At a meeting of 12 people shook hands. How many handshakes were at the same time?
2.21. On the chessboard of 64 squares randomly put two rooks black and white colors. What is the probability they will not be "beat" to each other?
3.21. The probability of hitting the target the first shooter in one shot is equal to 0.7, the second - 0.5. Find the probability that the target will be destroyed: a) two arrows; b) at least one gunner; c) Only one shooter.
4.21. The device consists of two units of the same type and the second type of three nodes. Reliable operation within the time T for the first node type is equal to 0.8, and the second node type - 0.7. a) Find the probability that a randomly selected node will work within the time T. b) Node worked warranty time T. What type he probably refers?
5.21. Among the parts manufactured work, on average, 2% of non-standard. Find the probability that among the test made at five parts: a) three non-standard; b) is the most probable number of non-standard parts (out of five); c) any non-standard parts.
6.21. The probability of occurrence of an event in each of the 900 independent trials is 0.5. Find the probability that the relative frequency of the event occurrence probability deviates from it by not more than 0.02.