Compute conditional occupancy across two rooms

Q: Compute conditional occupancy across two rooms

This question evaluates a data scientist's understanding of conditional probability and Bayesian updating, testing probabilistic reasoning and inference about joint occupancy states.

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Question

Probability and Bayes Update: Two Rooms

Setup

There are two rooms. Prior over occupancy states:

With probability 1/3: both rooms are occupied.
With probability 1/3: exactly one room is occupied.
With probability 1/3: both rooms are empty.

You pick one room uniformly at random to check.

Tasks

(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.

Compute conditional occupancy across two rooms

Probability and Bayes Update: Two Rooms

Setup

Tasks

Solution

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Compute conditional occupancy across two rooms

Overview

Probability and Bayes Update: Two Rooms

Setup

Tasks

Solution

Comments (0)