Favard length of a planar compact set K is the average length of its orthogonal projections. It has been known for a long time that given a nice enough self-similar set of dimension 1, such as the classical 4-corners Cantor set, its Favard length is zero. Let K be some nice fixed self-similar set of dimension 1, and let Kn denote the n-th step in the construction of K. Since the Favard length of K is zero, it follows that the Favard length of Kn converges to zero. What is the rate of convergence? This question, known as the "Favard length problem" or the "Buffon needle problem", was first posed by Peres and Solomyak in 2002, and it turned out to be remarkably difficult. To this day the precise rate of convergence has not been established for any self-similar set, and the gap between what is known, and what is conjectured, is very large. On the other hand, if you add a little randomness to the picture, things simplify immediately: there are precise estimates for the rate of convergence for various classes of random Cantor sets. In an ongoing work with Alan Chang and Giacomo Del Nin we prove first precise estimates for the Favard length of certain non-homogenous random Cantor sets. This seminar is meant to be a gentle introduction to the problem, and many open questions will be advertised.