Recall the airplane puzzle from the lab: the first person to get on the plane picks a random seat, the rest sit in their assigned seat if it is available, otherwise pick a random available seat....

Recall the airplane puzzle from the lab: the first person to get on the plane picks a random seat,  the rest sit in their assigned seat if it is available, otherwise pick a random available seat. Assume person i is assigned the seat i.

Suppose person 18 came in and discovered that their seat is taken.  Assuming that  the last person's seat, which is seat number n=32 on this plane,  it is still available, what is the probability that person 18 will randomly pick it?   Hint: to make sure your formula is correct, check that it works for the passenger right before the last one.

Enter your answer as a decimal number  with at most three digits after the decimal point, rounding if necessary.  For example, if your answer is 1/3, round it and enter it as 0.333,  if your answer is 2/3, enter it as 0.667, and if your answer is 1/2, enter it as 0.5.