Class 10 Maths Chapter 12 Review Exercise Solutions 2026 – Probability Notes PDF

Unit 12: Probability | Review Exercise | Punjab Board New Syllabus 2026–27

Updated August 2026: Review Exercise solutions for Probability have been uploaded below and are free to view or download, fully solved according to the new PCTB/PECTAA Class 10 Mathematics syllabus.

Testing the Whole Chapter at Once

Exercise 12.1 built the basic probability formula, Exercise 12.2 introduced the addition rule, and Exercise 12.3 introduced the multiplication rule. The Review Exercise removes those labels and mixes all three skills together, the way a real board paper naturally combines them inside a single probability question — and brings this entire Class 10 Mathematics syllabus to a close.

What This Review Exercise Draws On

Basic Probability and Complements

Quick-recall questions on the sample space, the probability formula, and complementary events, exactly as introduced in Exercise 12.1.

The Addition Rule

Mixed problems applying P(A or B) = P(A) + P(B) for mutually exclusive events, or the general version with the overlap subtracted, as covered in Exercise 12.2.

The Multiplication Rule

Problems applying P(A and B) = P(A) × P(B) for independent events, including both with-replacement and without-replacement scenarios, as covered in Exercise 12.3.

Step-by-Step Solved Examples

Q. No. 1: A card is drawn from a standard 52-card deck. Find the probability that it is a spade or a diamond.

These suits are mutually exclusive (a card can’t be both a spade and a diamond).

P(spade) = 13/52, P(diamond) = 13/52

P(spade or diamond) = 13/52 + 13/52 = 26/52 = 1/2

Q. No. 2: A bag has 5 red and 3 green balls. Two balls are drawn without replacement. Find the probability both are green.

First draw: P(green) = 3/8

After removing 1 green ball, 7 balls remain, with 2 green left.

Second draw: P(green | first green) = 2/7

P(both green) = 3/8 × 2/7 = 6/56 = 3/28

Q. No. 3: If P(A) = 0.5 and P(B) = 0.3, and A and B are independent, find P(A or B).

Since A and B are independent (not mutually exclusive), first find the overlap:

P(A and B) = P(A) × P(B) = 0.5 × 0.3 = 0.15

P(A or B) = P(A) + P(B) − P(A and B) = 0.5 + 0.3 − 0.15 = 0.65

These three questions are representative samples. The full PDF notes uploaded on this page walk through every question of the Review Exercise in the same numbered, step-by-step format.

MCQs, Short Questions & Long Questions from This Review

Alongside the main exercise, this page’s uploaded notes are organized the way Punjab Board papers are structured, so students can practice by question type:

• MCQs: Rapid-fire recall across all three exercises, useful for timed practice
• Short Questions: Two-step problems combining any two of the chapter’s core ideas
• Long Questions: Full multi-part problems that mirror the structure of an actual board exam question

Study Tips for Reviewing This Chapter

• Attempt the Review Exercise only after completing Exercises 12.1 through 12.3
• Keep both the addition rule and multiplication rule written together for quick reference, since Q. No. 3 above shows they can combine in a single question
• Practice identifying mutually exclusive vs. overlapping vs. independent events quickly, since this decision drives the whole solution
• Re-attempt any question you got wrong the next day, rather than only reading the correct answer once

Common Mistakes Students Make in This Review Exercise

• Trying to answer a multi-step question in one line instead of solving it stage by stage
• Mixing up when to add probabilities and when to multiply them
• Forgetting that independent events can still require the general addition rule (with overlap subtracted) when combined with “or”

Why This Exercise Matters for the Board Exam

Board papers rarely test a single probability rule in isolation, which is exactly what this Review Exercise simulates. Working through it carefully is one of the best ways to confirm genuine readiness for the Probability chapter — and, since this is the final chapter of the syllabus, for the full Class 10 Mathematics board exam.

Quick Links – Chapter 12: Probability

Links for sections other than the Review Exercise will be activated as they are published on this site.

Download Review Exercise Notes PDF

Click below to view or download the complete Review Exercise notes in PDF format.

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Frequently Asked Questions (FAQs)

Q1. Are these Review Exercise notes free to download?

Yes, all notes on this page are completely free to view and download in PDF format.

Q2. Which board are these notes for?

These notes are prepared according to the Punjab Board syllabus and are useful for all Punjab boards (Lahore, Gujranwala, Multan, Sargodha, Rawalpindi, Faisalabad, DG Khan, Bahawalpur, Sahiwal) as well as the Federal Board (FBISE).

Q3. When should I attempt the Review Exercise?

Only after completing all three exercises (12.1 to 12.3), since the questions here mix the basic probability, addition, and multiplication rules without labeling which exercise each one came from.

Q4. Does this page include MCQs and short questions too?

Yes, the uploaded notes include MCQs, short questions, and long questions covering the whole chapter, organized by question type to match the board paper pattern.

Q5. How can I download the PDF?

Click the “Download PDF” button above and the notes will open or download directly to your device.

Q6. Are these notes updated for the new 2026–27 syllabus?

Yes, these notes are prepared strictly according to the latest PCTB/PECTAA syllabus for the 2026–27 academic session.

Comments & Feedback

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