Chapter 12 Topics – Probability
Click on any topic to expand and view its exercises. Each section includes step-by-step solutions and real-world applications.
12.1 – Basic Probability Concepts
Random experiments, sample space, events, tree diagrams, possibility diagrams
This section introduces the fundamental concepts of probability: random experiments, outcomes, sample space, events, and their types. You'll learn to use tree diagrams and possibility diagrams to visualize sample spaces and calculate probabilities.
Sample space, events, tree diagrams
12.2 – Addition Law of Probability
Mutually exclusive events, Venn diagrams, union of events
This section covers the addition law of probability for both mutually exclusive and non-mutually exclusive events. You'll learn to use Venn diagrams to visualize events and calculate probabilities of unions.
Addition law, Venn diagrams
12.3 – Multiplication Law of Probability
Independent events, dependent events, conditional probability
This section covers the multiplication law of probability for independent and dependent events. You'll learn to calculate probabilities of combined events using conditional probability and distinguish between with and without replacement scenarios.
Multiplication law, conditional probability
Review Exercise 12
Complete revision and mixed practice problems
The review exercise mixes questions from all three sections of Chapter 12, giving you a chance to test whether you can move between topics without a hint about which method applies — a useful checkpoint before exams.
Complete Revision & Practice
Probability – What's Inside This Chapter
Chapter 12 – Probability is part of Class 10 Mathematics under the Revised National Curriculum 2023. Probability quantifies uncertainty in scientific research and finance. This unit covers basic probability concepts, compound events, conditional probability, and real-world applications in risk assessment, quality control, financial modeling, and data science.
Prepared by Muhammad Tayyab, Govt Christian High School Daska, this chapter's notes cover all 3 exercises plus the review exercise, with step-by-step solutions throughout.
✅ What This Chapter Covers
- ✓Basic concepts, compound events, conditional probability, real-world applications
- ✓Step-by-step solved exercises for all 3 sections
- ✓Based on the PECTAA syllabus
- ✓A complete review exercise for revision
- ✓Free access, no downloads required
🌐 Why This Chapter Matters
Probability quantifies uncertainty in scientific research and finance. This unit covers basic probability concepts, compound events, conditional probability, and real-world applications in risk assessment, quality control, financial modeling, and data science.
Mastering this chapter builds a foundation for higher studies and board exam success.
Related Chapter 12 Resources
📖 Definitions
Key terms and theorems for Chapter 12.
🧮 Formula Sheet
Probability formulas at a glance.
✅ Chapter MCQs
Practice multiple choice questions.
🎯 Guess Paper
Important questions predicted for exams.
🗂️ Past Papers
Solved previous board papers.
📔 Math Key Book
Full solution guide for all chapters.