Occupancy Problems in Quant Interviews
Occupancy problems interview prep for balls into boxes, empty boxes, collisions, expected occupied boxes, and sample-space mistakes.
Candidates preparing for combinatorics-probability hybrids.
What occupancy means
Occupancy problems place objects into boxes and ask about empty boxes, occupied boxes, collisions, or load. The objects and boxes are usually labeled in interview versions.
Clarify the random experiment
Before calculating, say whether each object chooses a box independently, whether boxes are equally likely, and whether objects are distinguishable.
Expected occupied boxes
A clean method is to define one indicator for each box being occupied. The expected number of occupied boxes is the sum of those occupation probabilities.
Collision questions
Collision questions ask whether two or more objects land in the same box. Birthday-style reasoning is often the right comparison.
Counting versus expectation
If the question asks for a probability distribution, counting may be needed. If it asks for an expected count, indicators are usually faster.
Common mistakes
Candidates often assume each occupancy pattern is equally likely. In many balls-into-boxes processes, different occupancy patterns can have different numbers of underlying assignments.
Practice the pattern
Use the LeetQuidity curriculum and calibration to turn this topic into a focused practice plan.