Question

There are n people in line, indexed by i=1,…,n , to enter a theater with n seats one by one. However, the first person ( i=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 n with equal probability. Every other person i=2,…,n that enters afterwards is sober and will take his assigned seat (seat i ) unless his seat i is already taken, in which case he will take a random seat chosen uniformly from the remaining seats.

Suppose that n=3 . What is the probability that person 2 takes seat 2?

(Enter a fraction or a decimal accurate to at least 3 decimal places.)

Answer 1

1/2
1/2