When boarding a plane, a line of \(n\) passengers was formed, each of whom has a ticket for one of the \(n\) places. The first in the line is a crazy old man. He runs onto the plane and sits down in a random place (perhaps, his own). Then passengers take turns to take their seats, and in the case that their place is already occupied, they sit randomly on one of the vacant seats. What is the probability that the last passenger will take his assigned seat?
Three friends decide, by a coin toss, who goes to get the juice. They have one coin. How do they arrange coin tosses so that all of them have equal chances to not have to go and get the juice?