Airplane Seat Probability Problem

You're one of 100 people standing in line to get onto an airplane that has 100 seats. There's a seat for every person, and each person has a boarding pass for an assigned seat. The first person to walk onto the plane drops his boarding pass and, instead of picking it up, takes a seat at random. Now, every other passenger will take either his assigned seat or, if that seat is taken, a random seat. You are the last passenger to walk onto the plane. There will be one seat left. What is the probability (in percentage) that you get to sit in your assigned seat?

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