A fully booked theatre is about to screen A Beautiful Mind to a group of100 mathemati- cians. the 1st mathematican was thinking about the Riemann
Hypothesis and somehow misplaced his ticket. As a consequence, he could not find the seat alloted to him and decided to sit at a random seat. From then on, any mathematician if he finds his seat oc- cupied, politely goes and seats at a random seat. What is the probability that the 100th mathematician seats in his own seat?