Compute conditional occupancy across two rooms
Company: Meta
Role: Data Scientist
Category: Statistics & Math
Difficulty: easy
Interview Round: Onsite
Two rooms may be occupied with the following priors: with probability 1/3 both rooms are occupied, with probability 1/3 exactly one room is occupied, and with probability 1/3 both are empty. You pick a room uniformly at random to check. (a) What is the probability the room you check is occupied? (b) Given you find your chosen room occupied, what is the probability the other room is also occupied? Show the Bayes calculation.
Quick Answer: This question evaluates a data scientist's understanding of conditional probability and Bayesian updating, testing probabilistic reasoning and inference about joint occupancy states.