  The education system for students in physics suffers (worldwide) from the
absence of a deep course in probability and randomness. This is the real
problem for students interested in quantum information theory, quantum optics,
and quantum foundations. Here the primitive treatment of probability and
randomness may lead to deep misunderstandings of theory and wrong
interpretations of experimental results. Since during my visits (in 2013 and
2014) to IQOQI a number of students (experimenters!) asked me permanently about
foundational problems of probability and randomness, especially inter-relation
between classical and quantum structures, this year I gave two lectures on
these problems. Surprisingly the interest of experiment-oriented students to
mathematical peculiarities was very high. This (as well as permanent reminding
of prof. Zeilinger) motivated me to write a text based on these lectures which
were originally presented in the traditional black-board form. I hope that this
might be useful for students from IQOQI as well as other young physicists.
