Its 50%. For 3 passengers the seating possibilities are {123,213,231,321}, so 3 gets to sit on seat 3 50% of the time. For 4 passengers the seating possibilit

Its 50%. For 3 passengers the seating possibilities are {123,213,231,321}, so 3 gets to sit on seat 3 50% of the time. For 4 passengers the seating possibilities are {1234,2134,2314,2341,2431,3241,3214,4231}, so 4 gets to sit on seat 4 50% of the time. From there you can do a proof by induction. If you like code: ---- import util.{Random=>rng} import collection.mutable.ArrayBuffer object passengers { def main(args:Array[String]) = { val n = args(0).toInt val simulations = args(1).toInt val happyLast = (1 to simulations).map(_=> { val seats = ArrayBuffer.fill[Int](n+1)(0) val taken = new ArrayBuffer[Int] val all = (1 to n).toSeq val seat = rng.shuffle(all).head seats(seat) = 1 taken += seat (2 to n).foreach( p=> { val seat = seats(p) match { case 0=> p case x=> rng.shuffle(all.diff(taken)).head } seats(seat) = p taken += seat }) seats(n) == n }) println( happyLast.filter(x=>x).size*1.0d/simulations ) } } ----- >scala -cp classes passengers 100 100000 >0.4997