A multinomial distribution (-1, Pi (1)), (0, Pi (2)), (1, Pi(3)), Pi(1)+ Pi(2) + Pi(3) = 1 is observed. Suppose that n(1) values -1, n(2) values 0 and n(3) values 1 (n = n(1) + n(2) + n(3)) were observed. The construction of the confidence region for the vector (Pi (1), Pi (2), Pi (3)) is given. Theoretical considerations are illustrated by an example of the results of a pool. NB due to the technical reasons the symbols used in abstract are not identical with those in original paper - see full content