15 Relative Frequency And Probability Examples And Worksheets - Maths Quest General Maths Preliminary Course Page 19
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30WORKED EXaMPLE 11
For the following probabilities, describe whether the event would be certain, probable, fi fty-fi fty,
unlikely or impossible.
4
18
0
a
b
c
9
36
THINK
WRITE
a
a
4
1
The event is unlikely as it has a probability of
is less than
and is therefore unlikely to
9
2
1
less than
.
occur.
2
b
A probability of 0 means the event is
b
The event is impossible as it has a probability
impossible.
of 0.
c
18
1
c
The event has an even chance of occurring as
= . Therefore, the event has an even
36
2
1
the probability =
.
chance of occurring.
2
WORKED EXaMPLE 12
In a batch of 400 televisions, 20 are defective. If one television is chosen, fi nd the probability of it not
being defective and describe this chance in words.
THINK
WRITE
1
There are 400 televisions (elements of the
sample space).
2
There are 380 televisions that are not defective
(number of favourable outcomes).
380
P(not defective) =
3
Write the probability.
400
19
=
20
4
1
It is very probable that the television chosen will
Since the probability is much greater than
and
2
not be defective.
very close to 1, it is very probable that it will not
be defective.
There are many situations where this will occur. You need to be able to recognise when you can
and cannot measure the probability. You cannot measure probability when each outcome is not
equally likely.
WORKED EXaMPLE 13
State whether the following statements are true or false, and give a reason for your answer.
1
The probability of correctly selecting a number drawn out of a barrel between 1 and 10 is
.
a
10
1
The weather tomorrow could be fi ne or rainy, therefore the probability of rain is
.
b
2
THINK
WRITE
a
a
Each outcome is equally likely.
True, because each number is equally likely to
be selected.
b
b
Each outcome is not equally likely.
False, because there is not an equal chance of
the weather being fi ne or rainy.
497
Chapter 15
Relative frequency and probability
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