Expected round of first selection in repeated sampling
Quick Overview
Evaluates expected first-selection round under sampling without replacement across employees. Strong answers map the process to a random permutation, show uniform round assignment, and compute the expected round as 50.5.
Expected round of first selection in repeated sampling
Company: Meta
Role: Data Scientist
Category: Analytics & Experimentation
Difficulty: medium
Interview Round: Onsite
Scenario: Ten of 1 000 employees are chosen each round for random perks. On average, which round sees your first selection?
Question 1: With 1 000 people and 10 selected per round without replacement, on average which round sees first selection? (Hint: hypergeometric distribution)
Quick Answer: Evaluates expected first-selection round under sampling without replacement across employees. Strong answers map the process to a random permutation, show uniform round assignment, and compute the expected round as 50.5.
There are 1,000 employees. Each round, 10 distinct employees are selected at random for a perk. No one can be selected twice before everyone has had a chance, so sampling is without replacement across rounds.
On average, in which round do you expect to be selected for the first time?
Constraints & Assumptions
The 10 employees in each round are distinct.
Across rounds, previously selected employees are not eligible again until all have been selected.
Every employee is equally likely to appear in any position of the random ordering.
There are exactly 100 rounds.
Clarifying Questions to Ask Guidance
Are there exactly 1,000 employees and 10 selected per round?
Does the process continue until everyone is selected once?
Are selections uniformly random among eligible employees?
Is the question asking expected round number or expected waiting time?
What a Strong Answer Covers Guidance
Recognizes the process as a random permutation of 1,000 employees split into blocks of 10.
Shows that your round is uniformly distributed over rounds 1 through 100.
Computes the expected round as (1 + 100) / 2 = 50.5.
Optionally derives the same result from the expected rank or hypergeometric reasoning.
Interprets the answer as halfway between rounds 50 and 51.
Follow-up Questions Guidance
What is the probability you are selected by round 20?
How would the answer change if 25 employees were selected per round?
What if employees could be selected again before everyone had a chance?