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
New 2026
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.
12.1
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Exercise 12.1
Sample space, events, tree diagrams
12.2 – Addition Law of Probability
Mutually exclusive events, Venn diagrams, union of events
New 2026
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.
12.2
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Exercise 12.2
Addition law, Venn diagrams
12.3 – Multiplication Law of Probability
Independent events, dependent events, conditional probability
New 2026
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.
12.3
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Exercise 12.3
Multiplication law, conditional probability
Review Exercise 12
Complete revision and mixed practice problems
New 2026
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.
R
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Review Exercise 12
Complete Revision & Practice
Probability – What's Inside This Chapter (PECTAA 2026)
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 2026 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 under the PECTAA 2026 syllabus.
Browse Notes by Individual Chapter
Each chapter also has its own dedicated page with exercise cards and full notes.
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Chapter 1: Complex Numbers
Complex number operations, Argand diagrams, and engineering applications with step-by-step solved exercises.
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Chapter 2: Quadratic Equations and Inequalities
Solving techniques, discriminant analysis, optimization applications, and real-world problem solving strategies.
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Chapter 3: Matrices and Determinants
Matrix operations, determinants, inverses, and computer graphics applications with complete solved exercises.
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Chapter 4: Functions and Graphs
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Chapter 5: Algebraic Fractions
Simplification, operations, solving equations, and engineering applications with detailed step-by-step solutions.
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Chapter 6: Vectors in Plane
Vector operations, dot product, and physics and engineering applications with practical solved problems.
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Chapter 7: Trigonometry
Trigonometric identities, equations, inverse functions, and real-world applications in architecture and navigation.
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Chapter 8: Chords and Arcs of a Circle
Relationships between chords, arcs, angles, and design and engineering applications for circular geometry.
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Chapter 9: Tangent and Angles of a Circle
Tangent properties, angle relationships, and geometry and design applications with construction techniques.
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Chapter 10: Practical Geometry of Circles
Geometric constructions, tangents, inscribed figures, and step-by-step methods for technical drawing.
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Chapter 11: Information Handling
Data collection, graphical representations, statistical analysis, and decision making for real-world problems.
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Chapter 12: Probability
Basic concepts, compound events, conditional probability, and real-world applications in risk assessment.
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Solved Exercises
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