Calculate Expected Meetings in Randomly Assigned Rooms

Q: Calculate Expected Meetings in Randomly Assigned Rooms

This question evaluates proficiency in probability theory, conditional expectation, and Bayesian reasoning applied to occupancy models, measuring a data scientist's competency in stochastic modeling and inference.

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Question

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?

Calculate Expected Meetings in Randomly Assigned Rooms

Random Assignment of Meetings to Rooms

Scenario

Questions

Solution

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