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Form
Chapter 9 Probability of Combined Events Mathematics 4

9.1 Combined Events Example 1

In an experiment, Fahmi chooses a number at
Describe combined events and list out the random from {1, 3, 4, 6} and Ganan chooses a
possible combined events number at random from {3, 6, 9}. Given A is the
event Fahmi chooses an even number and B is the
1. Combined event is the event that is produced event Ganan chooses an odd number.
from the union or intersection of two or more Describe, in words and listing, the outcomes of
events. each of the combined events.
(a) A and B (b) A or B
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Combined Event A or Event A and Solution:
event event B event B A = Event Fahmi chooses an even number
= {(4, 3), (4, 6), (4, 9), (6, 3), (6, 6), (6, 9)}
Notation A < B A > B B = Event Ganan chooses an odd number
A occurs or B = {(1, 3), (1, 9), (3, 3), (3, 9), (4, 3), (4, 9), (6, 3), (6, 9)}
Meaning occurs or both A Both A and (a) The combined event A and B is the event
B occur
Fahmi chooses an even number and Ganan
and B occur chooses an odd number.
A > B = {(4, 3), (4, 9), (6, 3), (6, 9)}
ξ ξ (b) The combined event A or B is the event Fahmi
A B A B
Venn chooses an even number or Ganan chooses
diagram an odd number.
A < B = {(1, 3), (1, 9), (3, 3), (3, 9), (4, 3), (4, 6),
(4, 9), (6, 3), (6, 6), (6, 9)}
Try question 1 in Formative Zone 9.1

BRILLIANT Tips Example 2
Combined event for three events A, B and C. A number is chosen at random from {10, 12,
(a) A < B < C 13, 15, 18, 20, 23, 24}. Given A is the event of
choosing a prime number, B is the event of
ξ choosing a multiple of 3 and C is the event of CHAP.
A B 9
choosing a number with the sum of digits greater
than or equal to 5.
List down all the outcomes for each of the
following combined events.
(a) A and C (b) B and C
(c) A or C (d) B or C

C Solution:
A = Event of choosing a prime number
(b) A > B > C = {13, 23}
B = Event of choosing a multiple of 3
ξ = {12, 15, 18, 24}
A B C = Event of choosing a number with the sum of
the digits greater than or equal to 5
= {15, 18, 23, 24}
(a) A and C = A > C
= {23}
(b) B and C = B > C
= {15, 18, 24}
C (c) A or C = A < C
= {13, 15, 18, 23, 24}
(d) B or C = B < C
= {12, 15, 18, 23, 24}
Try question 2 in Formative Zone 9.1

9.1.1 183

ENG09 Spotlight Matematik F4.indd 183 10/02/2021 11:17 AM