Slick solution from Tim Earl, a PhD student.
Let A be the first person and Z be the last.
Although there may be many misplaced people, the outcome is certain as soon as some passenger chooses to sit in the seat of either A or Z. At all times these seats are equally likely to be chosen by the currently displaced person.
Thus the probability that Z sits in the correct seat is 1/2.
Prof. G. J. G. Upton,
Professor of Statistics/Environmetrics
Dept of Mathematical Sciences/Centre for Environmental Science
University of Essex, Colchester, Essex. CO4 3SQ http://www.essex.ac.uk/maths/staff/upton/
Tel: 01206 873027; Sec:01206 872704; Fax: 01206 873043