Probability airport question code.

Question

Matthew Lozancich 2017-11-20

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/368017-probability-airport-question-code

回答： Torsten 2017-11-21

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

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Answer 1

Torsten 2017-11-21

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https://ww2.mathworks.cn/matlabcentral/answers/368017-probability-airport-question-code#answer_292380

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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;