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Can someone explain the answer to this question:

'Imagine there are a 100 people in line to board a plane that seats 100. The first person in line realizes he lost his boarding pass so when he boards he decides to take a random seat instead. Every person that boards the plane after him will either take their "proper" seat, or if that seat is taken, a random seat instead. Question: What is the probability that the last person that boards will end up in his/her proper seat.'

If instead of only the first person having lost their ticket the first two people have lost their tickets and take random seats?

Sam Whitehurst
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  • What have you tried? I suggest studying the classical solutions to the original problem to see if you can adapt the same arguments. Then, try it with smaller numbers. If you have $2$ people the answer is clearly $\frac 12$. What about $3$ people? $4$? Maybe you'll see a pattern which you could then try to prove. – lulu Mar 26 '19 at 20:36
  • For 2 people it is 1/3 and for 3 1/4 so should be a 1/n+1 relationship but I'm not fully sure how to prove this – Sam Whitehurst Mar 27 '19 at 09:01
  • and if only the 1st person has lost their ticket it should be 1/2 – Sam Whitehurst Mar 27 '19 at 09:02

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