Meetings randomly assigned to conference rooms

N rooms are available and K meetings are scheduled uniformly at random. Given that room 1 is not empty, what is the expected total number of meetings in room 1? Now assume two rooms where the trio of states {both occupied, exactly one occupied, both empty} are equally likely. Before entering, what is the probability the room you pick is occupied? If you enter and find it occupied, what is the probability the other room is also occupied?

Apply Bayes’ theorem and conditional expectations; the first part is a binomial conditioned on non-zero, the second uses the law of total probability.

Meta Data Scientist interview question: Calculate Expected Meetings in Randomly Assigned Rooms. {"blocks": [{"key": "20048950", "text": "Scenario", "type": "header-two", "depth": 0, "inlineStyleRanges": [], "entityRanges": [], "data": {...