Unit 12 Exercise 12.2 Class 10 Math Solutions – Probability, Punjab Board

Solved Unit 12 Exercise 12.2 for Class 10 Mathematics, Punjab Board. Complete step-by-step solutions covering the Addition Law of Probability for mutually exclusive and non-mutually exclusive events, union of events, and Venn diagram representations for Matric Part 2 students.

This page provides complete step-by-step solved solutions for Unit 12 Exercise 12.2: Probability, Class 10 Mathematics, Punjab Board (PCTB). It focuses on the Addition Law of Probability for mutually exclusive events P(A ∪ B) = P(A) + P(B), the generalized Addition Law for non-mutually exclusive events P(A ∪ B) = P(A) + P(B) - P(A ∩ B), and Venn diagram representations for Matric Part 2 examinations.
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Exercise Overview

Unit 12 Exercise 12.2 in Class 10 Punjab Board Mathematics focuses on compound probability calculations using the Addition Law of Probability. The exercise teaches students how to determine the probability of either of two events occurring (the union of events A and B, denoted as A ∪ B) under different relational scenarios.

Students explore two distinct mathematical formulations: when events A and B are mutually exclusive (disjoint, with no common outcomes), the addition theorem simplifies to P(A ∪ B) = P(A) + P(B). When events are non-mutually exclusive (overlapping, where A ∩ B ≠ ∅), the general theorem P(A ∪ B) = P(A) + P(B) - P(A ∩ B) is applied to eliminate double-counted intersection elements. Venn diagrams are utilized throughout to provide intuitive geometric visualizations of sample space partitions and event relationships.

In Punjab Board examinations (including BISE Lahore, Rawalpindi, Faisalabad, Gujranwala, Multan, Sargodha, Bahawalpur, and DG Khan), the Addition Law of Probability is a high-priority topic for Section A MCQs and Section B 4-mark short questions. Practicing these structured, step-by-step solutions guarantees algebraic precision and helps students secure top marks in board exams.

FAQs

Are these Unit 12 Exercise 12.2 solutions according to the Punjab Board syllabus?
Yes. These solutions strictly conform to the Punjab Curriculum and Textbook Board (PCTB) syllabus for Class 10 Mathematics for the 2026-2027 academic session.
What is the Addition Law of Probability for mutually exclusive events?
For two mutually exclusive events A and B (where A ∩ B = ∅), the addition law states that P(A ∪ B) = P(A) + P(B).
What is the Addition Law of Probability for non-mutually exclusive events?
For non-mutually exclusive events with common outcomes, the generalized addition law states that P(A ∪ B) = P(A) + P(B) - P(A ∩ B).
How are Venn diagrams used in Exercise 12.2?
Venn diagrams visually represent sample space S, event sets A and B, disjoint regions, and intersection overlaps (A ∩ B) to simplify probability calculations.
Do these notes cover all questions in Exercise 12.2?
Yes, all textbook questions in Unit 12 Exercise 12.2 are solved step-by-step with clear set notations, Venn diagrams, and probability derivations.
Why do we subtract P(A ∩ B) in the general addition theorem?
Subtracting P(A ∩ B) prevents double-counting the elements that belong to both events A and B simultaneously in the union A ∪ B.
Who should use these Class 10 Math Exercise 12.2 notes?
Class 10 Matric Part 2 students preparing for Punjab Board exams across Lahore, Rawalpindi, Faisalabad, Gujranwala, Multan, Sargodha, Bahawalpur, and DG Khan boards.
Can students read these Exercise 12.2 solutions online?
Yes, the complete solved PDF notes for Unit 12 Exercise 12.2 are freely available to read online on MaryamNotes.pk with high clarity.
Are these Unit 12 Exercise 12.2 solutions free for students?
Yes, all Class 10 Mathematics solutions and study resources on MaryamNotes.pk are 100% free to read online for all students.