Justice Mathews

Mathematics

25 October, 15:01

There are? people in line, indexed by?=1, ...,?, to with? seats one by one. However, the first person (?=1) in the line is drunk. This person has lost her ticket and decides to take a random seat instead of her assigned seat. That is, the drunk person decides to take any one of the seats 1 to? with equal probability. Every other person?=2, ...,? that enters afterwards is sober and will take his assigned seat (seat?) unless his seat? is already taken, in which case he will take a random seat chosen uniformly from the remaining seats. Suppose that?=3. What is the probability that person 2 takes seat 2? (Enter a fraction or a decimal accurate to at least 3 decimal places.)