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Official Data Lab

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STATLABAcademyStatistics through data and R practice

All STATLAB Academy lessons, quizzes, datasets, and notes are original or properly licensed. Textbooks may be used only as curriculum references.

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STATLAB Academy | Learn Statistics with R and Real-World Data

Lesson 12 of 16

Tree Diagrams and Sequential Events

Home/Modules/Module 5/Tree Diagrams and Sequential Events

Organize conditional branches, terminal outcomes, and total probabilities in sequential processes.

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46 minutes75% path

Learning objectivesBy the end of this lesson, students will be able to:

1Define the events and probability quantities used in tree diagrams and sequential events.
2Select and calculate an appropriate probability rule with a visible denominator or assumption.
3Interpret the result for a business decision without overstating certainty or causation.

Theory

Core probability reasoning

Organize conditional branches, terminal outcomes, and total probabilities in sequential processes.

Explanation 1

First-stage branch: An initial mutually exclusive outcome.

Explanation 2

Conditional branch: A second outcome probability given its path.

Explanation 3

Terminal probability: The product along a complete path.

Terminology

Concept map

First-stage branch

An initial mutually exclusive outcome.

Demand moves up, stable, or down.

Conditional branch

A second outcome probability given its path.

Correct signal given demand is up.

Terminal probability

The product along a complete path.

Up and correct signal.

Notation and formulas

Path probability

Key relationship

P(path) = product of conditional branch probabilities

Define every event before substituting values, then validate the result and denominator.

Step 1Check branches from each node sum to one.
Step 2Multiply along each path.
Step 3Add relevant terminal paths for the target event.

Interactive Mission

tree diagram builder

P(A)P(B given A)P(B given not A)

Terminal path	Joint probability
A then B	0.351
A then not B	0.099
not A then B	0.198
not A then not B	0.352
Total	1

Worked example

Demand signal tree

Scenario

A forecast signal has different accuracy for rising, stable, and falling demand.

Reversing a tree changes the conditional probabilities needed.

R connection

R note: Sequential Probability Trees

Run and edit the code, inspect intermediate output, and use the movable R Code Guide while practising.

Live R Lab

Sequential Probability Trees

Build a branch table, calculate terminal probabilities, and verify that they sum to one.

Editable R code

Results

Ready to run

Ready to run

Ready to run. Results, errors, tables, plots, and fallback messages will appear here.

Validate each branch pair.

Multiply along paths.

Confirm terminal probabilities sum to one.

Dataset provenance

Original synthetic data generated for STATLAB Academy. No textbook data used.

Interpretation safeguard

Branch probabilities must be conditional on the path that reaches that branch.

Reflection

Pause and write

Where could an unclear event definition or assumption change the conclusion in tree diagrams and sequential events?

Name the event, denominator, probability interpretation, and one operational limitation.

Assistant

Ask your probability coach

Help me reason through Tree Diagrams and Sequential Events by asking questions about my event definitions, denominator, formula choice, assumptions, and interpretation. Do not give a quiz answer before I submit.

Exit check

Lesson checkpoint

Use a hint before submitting if needed. Full calculations and interpretations appear after submission.

Checkpoint

Module 5 Lesson 12 Checkpoint

Question 1 of 2. Answered 0/2. Passing score: 70%.

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Question 1: Numeric answer

mediumCalculate and responsibly interpret probability for a defined event.

A first branch has probability 0.4 and its conditional second branch has probability 0.7. Find the terminal probability.

Resource

Recommended reading

Explore additional probability explanations and exercises from properly licensed or publisher resources.

Resource

Module 5 learning material

Download an original worksheet or guide for this lesson.

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