# Probabilistic Parking Spaces

A row of street parking has spaces numbered 1 through 100, in that order. Each person trying to park drives by the spaces one-by-one starting at number 1.

At each open space, they are told how many open spaces, $$S,$$ they haven't passed (including the current space). They park in that space with probability $$\frac{1}{S};$$ otherwise, they move on to the next open space.

What is the expected value for the parking spot of the $$100^\text{th}$$ person to arrive (assuming no one has left and only one car goes through the parking process at a time)?

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