Expected meetings in Room 1 after random assignment

Q: Expected meetings in Room 1 after random assignment

This question evaluates probability and statistical reasoning skills, focusing on conditional expectation and discrete probabilistic modeling in a balls‑in‑bins context and falls under the Analytics & Experimentation domain for Data Scientist roles.

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Question

Randomly Assigned Meetings Across Rooms (Balls-in-Bins)

Setup

There are N rooms and k meetings.
Each meeting independently chooses a room uniformly at random (multiple meetings can be in the same room).
Let X₁ be the number of meetings assigned to Room 1.

Question

Given that Room 1 is non-empty (i.e., X₁ ≥ 1), what is the expected number of meetings in Room 1, E[X₁ | X₁ ≥ 1]?

Hint: Use conditional probability and linearity of expectation.

Expected meetings in Room 1 after random assignment

Randomly Assigned Meetings Across Rooms (Balls-in-Bins)

Setup

Question

Solution

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