Expectation · College cafeteria
Nobody sits next to a stranger
A cafeteria bench has 10 seats in a row, all empty. Students arrive one at a time, and nobody will sit directly next to someone already seated. Each new student picks uniformly at random among the seats that are empty and have no occupied neighbor. Students keep arriving until no such seat is left. What is the expected number of students on the bench at the end?
Answer with an expected value. First lock in a gut guess with an 80% range, then solve it properly, then watch a simulation settle on the truth.
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