Independent and Dependent

Events

19

19.1 Introduction

EMBEG

In probability theory events are either independent or dependent. This chapter discusses thediffer-

ences between these two categories of events and will show that we usedifferent sets of mathematical

rules for handling them.

See introductory video:VMgdw at http://www.everythingmaths.co.za

19.2 Definitions

Two events are independent if knowing something about the value ofone event does not give any

information about the value of the second event.For example, the event of getting a ” 1 ” when a die is

rolled and the event of getting a ” 1 ” the second time it is thrown are independent.

The probability of two independent events occurring, P(A∩ B), is given by:

P(A∩ B) = P(A)× P(B) (19.1)

DEFINITION: Independent events

Events are said to be independent if the resultor outcome of one event does not

affect the result or outcome of the other event. So P(A/C) = P(A), where P(A/C)

represents the probability of event A after event C has occurred.

Example 1: Independent Events

QUESTION

What is the probabilityof rolling a 1 and then rolling a 6 on a fair die?

SOLUTION