Probability airport question code.

So I've been working on this problem for hours and now I'm stuck.. I can't figure it out. I know my probability is messed up, in fact I think it should be around 50%?

You are at the airport waiting in line to board a plane. There are 99 other passengers and unfortunately for you, you are last in line. At the front of the line you recognize a colleague, Frank. Frank is known to randomly sit where he pleases instead of his assigned seat. All the other passengers, including yourself, behave in a more sane fashion:

• They will look to sit in their assigned seat, if that seat is available, theywill sit in their assigned seat.
• On the other hand, if their assigned seat is taken, they will pick a free seatat random to sit in.
• Create a function that runs a 10,000 iteration Monte Carlo simulation that estimates the probability that your seat will be taken

function boarding
  %100 passangers, so assuming we have 100 seats
  %Frank has a 1 percent chance of sitting in his assigned set if he picks at
  %random

    trials = 10000;
    P=100;
    inmyseat=0;
    x=0;
    for i=1:trials
    x=randi([1,100],1);

    if x==1  %if x==1 then it means Frank sat in his own seat
        break
    else
        for P=(99:-1:2)
            y=randi([1,P],1);

            if y==1 %this means that if y==1 then they sat in my seat
               inmyseat = inmyseat+1;
               break
            end

        end
    end
    end

    prob=(inmyseat/trials)*100

    end

Answer 1

[Torsten]

function boarding
%100 passengers
%We assume that Frank's seat is seat 99, your seat is seat 100.
%Further assume that seat i belongs to passenger i+1 (i=1,...,98)
trials = 10000;
P = 100;
inmyseat = 0;
for i=1:trials
  outcome = 0;
  start = 1;
  while outcome == 0
    x = randi([start,P],1);
    if x == P-1
      outcome = 1;
      inmyseat = inmyseat+1;
    elseif x == P
      outcome = 1;
    end 
    start = x+1;
  end 
end
prob = inmyseat/trials*100;

Best wishes

Torsten.