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  • CS202: Discrete Structures
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  • Conditional Probability
    Course Introduction
    Course Syllabus
    Unit 1: Sets, Set Relations, and Set Functions
    1.1: Set Notation and Relations
    Set Notation and Relations
    Notation
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    1.2: Basic Set Operations
    Basic Set Operations
    Types of Sets
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    1.3: Cartesian Products and Power Sets
    Cartesian Products and Power Sets
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    1.4: Summation Notation and Generalizations
    Summation Notation and Generalizations
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    Unit 1 Assessment
    Unit 1 Assessment
    Unit 2: Counting Theory
    2.1: Rule of Products
    Introduction to the Rule of Products
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    2.2: Permutations
    Ordering Elements of a Set
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    2.3: Partitions of Sets and the Law of Addition
    Partitions and Addition Laws
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    2.4: Combinations and the Binomial Theorem
    Combinations and the Binomial Theorem
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    Unit 2 Assessment
    Unit 2 Assessment
    Unit 3: Mathematical Logic
    3.1: Propositions and Logical Operators
    Propositional Logic
    Propositions and Logical Operators
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    3.2: Truth Tables and Propositions Generated by a Set
    Summary of Logic Notation
    Truth Tables and Propositions Generated by a Set
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    3.3: Equivalence and Implication
    Equivalence and Implication
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    3.4: The Laws of Logic
    The Laws of Logic
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    Unit 3 Assessment
    Unit 3 Assessment
    Unit 4: Mathematical Induction and Proofs
    4.1: Mathematical Systems
    Mathematical Systems
    4.2: Direct Proof
    Direct Proof
    4.3: Indirect Proof
    Indirect Proof
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    4.4: Propositions over a Universe
    Propositions and Truth Sets
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    4.5: Mathematical Induction
    Discussion and Examples
    4.6: Strong Induction
    Strong Mathematical Induction
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    Unit 4 Assessment
    Unit 4 Assessment
    Unit 5: Probability
    5.1: Introduction
    Introduction to Discrete Probability
    5.2: Sample Spaces, Events, and Their Probabilities
    Sample Spaces, Events, and Their Probabilities
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    5.3: Complements, Intersections, and Unions
    Complements, Intersections, and Unions
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    5.4: Conditional Probability and Independent Events
    Conditional Probability
    Independent Events
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    Unit 5 Assessment
    Unit 5 Assessment
    Unit 6: Recursion
    6.1: Introduction
    Recursion Demystified
    Recursive Definitions
    6.2: Transitioning from Informal to Formal
    Collected Definitions of Recursion
    Explanation and Examples
    Illustrating Recursion
    Sequences and Recursion
    6.3: The Many Faces of Recursion
    The Many Faces of Recursion
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    6.4: Sequences
    Sequences
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    6.5: Recursion in the Real World
    Predicting Data Sample Values
    Unit 6 Assessment
    Unit 6 Assessment
    Unit 7: Graphs
    7.1: A Less-Formal Introduction
    Basic Graph Theory
    7.2: A Formal Introduction
    Introduction to Graphs
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    7.3: Graph Structures
    Data Structures for Graphs
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    7.4: Graph Node Connectivity
    Connectivity
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    7.5: Graph Traversals
    Traversals: Eulerian and Hamiltonian Graphs
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    7.6: Graph Optimization
    Graph Optimization
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    7.7: Planarity and Colorings
    Planarity and Colorings
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    Unit 7 Assessment
    Unit 7 Assessment
    Unit 8: Trees
    8.1: Introduction
    Quick Introduction to Trees
    Formal Introduction to Trees
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    8.2: Spanning Trees
    Overview of Spanning Trees
    Detailed Discussion of Spanning Trees
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    8.3: Rooted Trees
    Rooted Trees
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    8.4: Binary Trees
    Binary Trees
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    Unit 8 Assessment
    Unit 8 Assessment
    Unit 9: Finite-State Automata
    9.1: Introduction
    Finite-State Machine Overview
    More on Finite State Machines
    State Machines
    9.2: State Transition Diagrams
    State Transition Diagrams
    9.3: Finite-State Machine States
    FSM States
    FSM Examples
    9.4: Putting the Basics to Use
    Putting the Basics to Use
    Unit 9 Assessment
    Unit 9 Assessment
    Study Guide
    CS202 Study Guide
    Course Feedback Survey
    Course Feedback Survey
    Certificate Final Exam
    CS202: Certificate Final Exam
    Proctor-Verified Final Exam
    Archived Materials
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  1. CS202: Discrete Structures
  2. Unit 5: Probability
  3. 5.4: Conditional Probability and Independent Events
  4. Conditional Probability

Conditional Probability

Completion requirements

Events can be dependent or independent of something else. This video considers events whose probability of occurrence is independent of all other events.

 

Source: Albert R. Meyer, https://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-042j-mathematics-for-computer-science-spring-2015/probability/tp11-2/
 Creative Commons License This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 License.

Last modified: Friday, 26 January 2024, 12:30 PM
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Saylor Academy © 2010-2025 except as otherwise noted. Excluding course final exams, content authored by Saylor Academy is available under a Creative Commons Attribution 3.0 Unported license. Third-party materials are the copyright of their respective owners and shared under various licenses. See detailed licensing information. Saylor Academy®, Saylor.org®, and Harnessing Technology to Make Education Free® are trade names of the Constitution Foundation, a 501(c)(3) organization through which our educational activities are conducted.