Page 345 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_ENGLISH

Statistical Methods in Economics Dilfraz Singh, Lovely Professional University

Notes Unit 27: Additive and Multiplicative Law of Probability

CONTENTS
Objectives
Introduction
27.1 Additive Rule of Probability
27.2 Multiplicative Rule of Probability: Conditional Probability
27.3 Summary
27.4 Key-Words
27.5 Review Questions
27.6 Further Readings

Objectives

After reading this unit students will be able to:
• Discuss Additive Rule of Probability.
• Explain Multiplicative Rule of Probability: Conditional Probability.
Introduction

Often it is easier to compute the probability of an event from known probabilities of other events.
This can be well observed if the given event can be represented as the union of two other events or
as the complement of an event. Two such rules used for simplifying the computation of probabilities
of events are:
1. Addition Rule of Probability
2. Multiplication Rule of Probability

27.1 Addition Rule of Probability

For any two events A and B
)
(
−
PA ∪ B = P (A) + P (B) PA ∩ ( B ) ... (1)
or P (A or B) = P (A) + P (B) – P (A and B) ... (2)
)
In case A and B are mutually exclusive events, then ( PA ∩ B = 0 and the addition rule of probability
in (1) becomes
(
)
PA ∪ B = P (A) + P (B) ... (3)
Proof: For any two events A and B, we can write
A= ( B )A ∩ ( A ∩ B )

∴ P (A) = ( PA ) ( ∩ ∩ B + PA B ) ... (a)

Using axiom (iii) of probability as the events ( B and ( )A ∩ B are mutually exclusive.
) A ∩

340 LOVELY PROFESSIONAL UNIVERSITY