Constructing adequate probability models is a basic problem in studies of controlled evolutionary systems. Three approaches are known nowadays to construct models of such systems. There are some disadvantages of the existing approaches and another approach, based on cybernetics, is proposed. Some features of the cybernetic approach are demonstrated in this paper by solving the well-known independence paradox. 2010 Mathematics Subject Classification. Primary 60K99, 93C99. License or copyright

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... trictions may apply to redistribution; see http://www.ams.org/journal-terms-of-use 134 M. A. FEDOTKIN answers in a row. A student gives a correct answer to the professor with probability p and does the same to the assistant professor with probability q > p. A student is asked to choose between one of two sequences of answering the questions: 1) professorassistant professor-professor (P-AP-P), or 2) assistant professor-professor-assistant professor (AP-P-AP). Let us consider the core of the solution of this instructive problem which was proposed in [4, 5] . Suppose that A 1 , A 2 , A 3 denote the events that a student succeeds in answering the first question to the professor, the second question to the assistant professor, the third question to the professor, respectively, and let A stand for the event that a student passes the exam under behavior pattern P-AP-P. We introduce similar notation for the behavior pattern AP-P-AP, namely let B 1 , B 2 , and B 3 denote the events that a student succeeds in answering the first question to the assistant professor, the second question to the professor, the third question to the assistant professor, respectively, and let B stand for the event that a student passes the exam under behavior pattern AP-P-AP. Then netics, issue 9, "Fizmatgiz", Moscow, 1963, pp. 5-22. (Russian)