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Calculate Expected Meetings in Randomly Assigned Rooms
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Jul 12, 2025, 6:59 PM
Data Scientist
Onsite
Statistics & Math
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Random Assignment of Meetings to Rooms
Scenario
There are N rooms and K meetings. Each meeting independently chooses a room uniformly at random (probability 1/N per room).
Questions
Given that room 1 is not empty (i.e., has at least one meeting), what is the expected number of meetings in room 1?
Now consider only two rooms and suppose the three macro-states are equally likely a priori: {both occupied, exactly one occupied, both empty} each with probability 1/3.
(a) Before entering, if you pick a room uniformly at random, what is the probability it is occupied?
(b) If you enter and find your chosen room occupied, what is the probability the other room is also occupied?