Deduction of quantum theory and its extensions from classical probability

For more than 30 years quantum probability (QP) has been considered as a generalization of classical probability (CP). Now we understand that this is not true: QP is a deeper level of CP. Main goal of the talk is to explain the statement above and why, now and in the future, the best way to introduce people to quantum mechanics and its natural extensions is a course in classical probability. If time permits, some feed-back of this new approach, for classical probability, will be illustrated through some examples.