Airplane Boarding: Last Passenger's Seat

Hard probability interview practice: Airplane Boarding: Last Passenger's Seat.

100 passengers are waiting to board a plane with exactly 100 seats. Each passenger has a ticket for a specific seat (passenger $n$ has ticket for seat $n$). The **first passenger is crazy** and sits in a random seat (uniformly chosen from all 100 seats). Each subsequent passenger: - Sits in their assigned seat if it's available - Otherwise, picks a random available seat What is the probability that the **100th (last) passenger** sits in their assigned seat (#100)?

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