Page 157 - Mathematics Coursebook

16.3 Mutually exclusive outcomes

16.3 Mutually exclusive outcomes

A bag contains sweets of di$erent colours.
One sweet is taken from the bag. !is is an event.
Here are two possible outcomes.
A red sweet is taken out. A green sweet is taken out.
!ese are mutually exclusive outcomes. !ey cannot both happen at the same time.
Here are two more possible outcomes.
A yellow sweet is taken. !e sweet taken tastes of lemons.

!ese are not mutually exclusive outcomes. !e sweet could be yellow and taste of lemons.

Worked example 16.3

A wallet contains $5, $10, $20 and $50 notes. One note is taken from the wallet. Here are three
possible outcomes.
Outcome A: An amount of $5 is taken.
Outcome B: An amount of $10 or less is taken.
Outcome C: An amount of $20 or more is taken.
Which of these pairs of outcomes are mutually exclusive?
a A and B b A and C c B and C

a A and B are not mutually exclusive. A means a $5 note is taken.
B means a $5 or a $10 note is taken.
$5 could be taken in either case.
b A and C are mutually exclusive. A means a $5 note is taken.
C means a $20 or $50 note is taken.
These have nothing in common.
c B and C are mutually exclusive. B means a $5 or a $10 note is taken.
C means a $20 or $50 note is taken.
These have nothing in common.

) Exercise 16.3

1 Aiden has these coins in his pocket.
He takes out one coin at random. 10 10
Here are four possible outcomes. 10 10 20 20 50 50 $1
A: He takes out 10 cents. 10 10 20 20
B: He takes out 20 cents or less. 10 10
C: He takes out 20 cents. 20 20 50 50
D: He takes out 50 cents or more.
a Find the probability of:
i outcome A ii outcome B iii outcome C iv outcome D.
b Which of these are mutually exclusive?
i A and B ii A and C iii B and C iv B and D v A, C and D

156 16 Probability