Solve the following problems (1 - 6)

1.2. Five passengers sit in a train consisting of 10 cars. Each passenger is equally likely to sit in any of the 10 cars. Determine the number of all possible variants of accommodation of passengers on the train.

2.2. Cube, all of whose faces are painted, sawed per thousand cubes of the same size. These cubes are thoroughly mixed. Determine the probability that the extracted random cube will have two colored faces.

3.2. At the factory of concrete products manufactured panels, of which 90% - the highest grade. What is the probability that a randomly selected from three panels of the premium will be: a) the three panels; b) at least one panel; c) no more than one panel?

4.2. Details on the processing of fall into one of three machines with probabilities equal to 0.2, respectively; 0.3; 0.5. Probability of marriage on the first machine is equal to 0.02, in the second - 0.03, in the third - 0.01. Find: a) the probability that a randomly taken after processing detail - standard; b) the probability of treatment taken at random items on the second machine, if it was a standard.

5.2. In the family of four children. Taking equally probable birth of a boy and a girl, find the probability that the boys in the family: a) three; b) at least three; at two.

6.2. The probability of occurrence of an event in each of the independent trials is 0.8. Find the probability that in 144 trials event occurs 120 times.

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