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There are 100 passengers lined up (in a random order) to board a plane. The plane is fully booked, meaning there are exactly 100 seats available. Due to a technical malfunction, the first passenger chooses a seat at random, with all seats equally likely. Each of the other passengers then proceeds as follows: if their assigned seat is free, they will sit in it; otherwise, they will take a random available seat. What is the probability that the last passenger will sit in their assigned seat? This classic brain teaser, often referred to as the "100-seat airplane problem," is a favorite in interviews at top tech companies (like Google, Amazon, and Meta) and finance firms (like hedge funds and investment banks). Why? Because it tests your ability to think probabilistically, reason recursively, and break down seemingly complex problems into simple patterns. Note: Add your answers in the comment section.