Getting Started

Welcome Who am I? Coding Assessment

Introducing Mathematics

Course Introduction Challenges

Numerical Systems

Introduction Positional Notation Converting Between Bases Binary Addition Binary Multiplication Challenges (Python) Challenges (Java)

Modular Arithmatic

Introduction The Modulus Operator Cyphers Modular Arithmetic Modular Inverse Challenges (Java)

Algorithms

Introduction Algorithms Time Functions Asymptotic Complexity Summation Challenges

Propositional Logic

Introduction Propositional Logic Conjunction and Disjunction Implication and Equivalence Bitwise Operators Challenges

Set Theory

Introduction Sets Subsets and Supersets Set Operations Challenges

Graph Theory

Introduction Graphs Directed Graphs Structure of Language Search Trees Neural networks Game Object Trees Challenges Graph Question Generator

Proof

Introduction Proof Proof by Cases Proof by Contradiction Proof by Induction Challenges

Maths to Code

Maths to Code Challenges Question Generator

Descriptive Statistics

Introduction Statistics Measures of Central Tendency Measures of Spread Data Visualisation Correlation Challenges

Probability

Introduction Probability Basics Combinatorics Probability Trees Law of Total Probability Bayes Rule Challenges

Inferential Statistics

Introduction Probability Distributions Samples and Populations Hypothesis Testing Z Scores Student's T-Test Challenges

Probability Trees

In this section we’re going to see how to use probability trees to visualise conditional probabilities.

Watch the video and then answer the questions below.

Ten-minute video

You can also view this video on YouTube

Key Points

We can represent a sequence of decisions as a decision tree. If we attach probabilities to each choice, we get a probability tree.

Each choice is labeled with it’s conditional probability, i.e. “given you’ve got here in the tree, what is the chance you’ll pick this choice”.

To find the probability of a particular path through the decision tree (i.e. that a specific sequence of decisions is made), you multiply along the branches.

Because paths are mutually exclusive, you can add their probabilities to find their joint probability.

Summary

In this section we saw probability trees.

In the next section we look at the Law of Total Probability.

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