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Meta/ Facebook Probability Interview Questions for data scientists
출처 : https://leonwei.com/meta-facebook-probability-interview-questions-for-data-scientists-f307a412ea20

Ads Serving:
There are two different ads serving mechanisms for the Facebook newsfeed.
The first is randomly replacing a feed with an advertisement with a probability of 4%.
The second is: every 25 feeds, turn one of them into an ad. Question 1: What is the expected number of ads shown in 100 news stories for each option? Variance?

Sample Answer:
Binomial distribution: p=0.04, n=100, E= np = 4, V=n*p*(1-p) =3.84
E=4, V=0

Question 2: Probability of seeing more than twice as many expected value times of ads for both algorithms?
Question 3: What are the maximum number of back-to-back ads for both algorithms?
Question 4: What are the expected number of back-to-back ads for both algorithms?
Question 5: What are the probability of seeing back-to-back ads for both algorithms?

Conference Rooms
There are N conference rooms, and M meetings are randomly assigned to each room.
Question: If we already know that room #1 has been assigned at least one meeting, what is the expected number of meetings that were assigned to room #1?

Drawing a user
Question 1. 1000 people, each time we select 10 users with replacement, on average, how many times before a specific user is drawn?

Question 2: 1000 people, each time we select 10 users without replacement, on average, how many times before a specific user is drawn?
Fake news
About 2% of news is fake news, 98% are non-fake news. There is a fake news detection model with 95% accuracy of correctly identifying either fake or non-fake news.
Question: What is the actual probability if a piece of news is predicted as fake news?


Daily comments distribution
Question 1: Every day, we count the total number of comments on Facebook. What is the daily number of comments distribution that may look like?
Question 2: draw the distribution on a whiteboard
Ads reviewer
20% of reviewers are lazy reviewers who always approve an ad without carefully reviewing them.
80% of reviewers are good reviewers who give 60% of ads approvals and 40% rejections.
Q1: The overall probability of a new ad being approved.
Q2: If an ad is rejected, what is the probability that it’s reviewed by a lazy reviewer?
Q3: Expected number of approved ads every 100 ads.
Q4: A reviewer gave 3 good reviews, probability of them being a lazy reviewer