Discrete Mathematics Level 4

In a queue, 100 passengers are waiting for the shipment in a airplane.

Each of them has a ticket for each of the 100 seats in the airplane. (For convenience, let's say the passenger n in the queue has a ticket for the seat number n )

Unfortunately, the first person in line is mad, and will ignore the seat number on their ticket, picking a random seat to occupy. All other passengers are quite normal, and go to their proper places, unless it is already occupied. If it is occupied, they will find a free place to sit, randomly.

What is the probability (in %) that the person 100, being the last to board the airplane will sit in seat 100?


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