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Exercise: Consider a theater with $n$ seats that is fully booked for this evening. Each of the $n$ people entering the theater (one by one) has a seat reservation. However, the first person is absent-minded and takes a seat at random. Any subsequent person takes his or her reserved seat if it is free and otherwise picks a free seat at random.

(i) What is the probability that the last person gets his or her reserved seat?

(ii) What is the probability that the $k$th person gets his or her reserved seat?

I get $p = 0.5$ for (i), but I have no idea if it's right.

Can somebody help me with (i) and especially (ii)?

Thank you!

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  • $\begingroup$ I would say advanced (graduate level?) probability. $\endgroup$
    – Ystar
    Commented Feb 28, 2015 at 3:01
  • $\begingroup$ I suggest you search MSE for "taking seats on a plane." $\endgroup$
    – André Nicolas
    Commented Feb 28, 2015 at 3:06
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    $\begingroup$ Check Byron Schmuland's answer for $ii)$ $\endgroup$
    – user142198
    Commented Feb 28, 2015 at 3:10
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    $\begingroup$ @Committing to a challenge : Thanks, that's it! $\endgroup$
    – Ystar
    Commented Feb 28, 2015 at 3:14

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