Unit 12 Exercise 12.3 Class 10 Math Solutions – Probability, Punjab Board

Solved Unit 12 Exercise 12.3 for Class 10 Mathematics, Punjab Board. Complete step-by-step solutions covering the Multiplication Law of Probability for independent events and dependent events (with and without replacement) for Matric Part 2 students.

This page provides complete step-by-step solved solutions for Unit 12 Exercise 12.3: Probability, Class 10 Mathematics, Punjab Board (PCTB). It covers the Multiplication Law of Probability for independent events P(A ∩ B) = P(A) × P(B) and dependent events P(A ∩ B) = P(A) × P(B|A), sampling with and without replacement, and joint probability calculations for Matric Part 2 examinations.
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Exercise Overview

Unit 12 Exercise 12.3 in Class 10 Punjab Board Mathematics covers joint probability calculations using the Multiplication Law of Probability. The exercise develops students' proficiency in calculating the probability of the simultaneous or sequential occurrence of two events (the intersection A ∩ B).

The exercise systematically distinguishes between independent events and dependent events. When events A and B are independent (the outcome of event A does not alter the likelihood of event B), the product rule P(A ∩ B) = P(A) × P(B) applies (such as successive dice rolls or drawing with replacement). When events are dependent, the outcome of event A modifies the sample space for event B, requiring conditional probability: P(A ∩ B) = P(A) × P(B|A) (such as drawing cards or colored marbles without replacement).

In Punjab Board examinations (BISE Lahore, Rawalpindi, Faisalabad, Gujranwala, Multan, Sargodha, Bahawalpur, and DG Khan), Multiplication Law problems are classic 4-mark short questions and frequent multiple-choice items. Practicing these structured, step-by-step solutions ensures mathematical accuracy and enables students to score top marks in Matric Part 2 board exams.

FAQs

Are these Unit 12 Exercise 12.3 solutions according to the Punjab Board syllabus?
Yes. These solutions strictly adhere to the Punjab Curriculum and Textbook Board (PCTB) syllabus for Class 10 Mathematics for the 2026-2027 academic session.
What is the Multiplication Law of Probability for independent events?
For two independent events A and B, the multiplication law states that the joint probability of both events occurring is P(A ∩ B) = P(A) × P(B).
What is the Multiplication Law of Probability for dependent events?
For two dependent events A and B, the multiplication law states that P(A ∩ B) = P(A) × P(B|A), where P(B|A) is the conditional probability of B occurring given A has occurred.
How does sampling with and without replacement affect probability?
Sampling with replacement keeps events independent because the sample space size remains constant; sampling without replacement makes events dependent as sample size and composition change.
Do these notes cover all questions in Exercise 12.3?
Yes, all textbook problems in Unit 12 Exercise 12.3 are solved step-by-step with clear probability product formulas and verified numerical fractions.
How do we identify whether two events are independent or dependent?
Events are independent if the occurrence of one has no influence on the chance of the other occurring; otherwise, they are dependent.
Who should use these Class 10 Math Exercise 12.3 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 12.3 solutions online?
Yes, the complete solved PDF notes for Unit 12 Exercise 12.3 are freely available to read online directly on MaryamNotes.pk.
Are these Unit 12 Exercise 12.3 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.