An airplane has 100 passengers. But the very first one to get on is missing his ticket! He just takes a random seat, and refuses to move from that spot.
The rest of the passengers board the plane one by one. Each passenger takes the correct seat, unless it's already taken. If their seat is already taken, they sit in a random seat, and refuse to move.
What's the probability that the last passenger gets the correct seat?
(Hint: First try to consider an airplane with 2 or 3 passengers)
It turns out that the first passenger isn't isn't really confused, he's malicious! He knows where he's supposed to sit, and intentionally sits anywhere but there. What's the probability that the last passenger gets the correct seat?
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