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Probability: Expected Time for \(n\) people to leave an elevator

I wondered about this when thinking about a more specific case. Consider that 3 people are all on an elevator and each person is equally likely to stay or exit the elevator at each stop. (So, for example, the elevator could stop while no one leaves). What is the expected number of stops before everyone leaves the elevator?

From this, I wanted to determine the expected number of stops for \(n\) people to leave the elevator. Anyone have any ideas?

Probability
Expected Value
Random Variable

Note by Oli Hohman
6 months, 2 weeks ago

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you actually cannot solve it as it may be actually having infinite number of stops you can only tell the probability of number of people exiting at a particular stop and we would have to solve according to the problem Aniket Jain · 4 months ago

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