Year 10A Mathematics
Chapter 8 Probability
Content descriptions for Substrand Chance
 Describe the results of two- and three-step chance experiments, both with and without replacements, assign
probabilities to outcomes and determine probabilities of events. Investigate the concept of independence
(ACMSP246)
 Use the language of ‘if ....then, ‘given’, ‘of’, ‘knowing that’ to investigate conditional statements and identify
common mistakes in interpreting such language (ACMSP247)
 (10A) Investigate reports of studies in digital media and elsewhere for information on their planning and
implementation (ACMSP277)
Learning Goals and Success criteria
Topic
Learning Goals
To:
Success Criteria
I can
8.1 Review
of
probability
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Define and understand the terms:
trial, experiment, event, sample space, outcome
Know the probability values assigned to
impossible, certain, likely, unlikely and equally
likely events
All probability values follow 0≤Pr(A)≤1
Understand the difference between
experimental probability and theoretical
probability
Determine probabilities using
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8.2 Unions
and
intersections
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Understand and calculate long run proportion
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Define and understand the terms: sets, union,
intersection, complement, complementary
events, mutually exclusive events, empty(null)
set and universal set as applied to Venn
Diagrams, Karnaugh Maps(Two-way Tables) and
probability calculations
Learn and apply the symbols/set notation for
intersection, union, complement, elements,
mutually exclusive events, empty(null) set and
universal set to set theory and Probability
calculations
Learn how to convert information in a Venn
diagram to a Karnaugh diagram and vice-versa
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8.3 The
addition rule
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8.4
Conditional
probability
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Learn and apply the addition rule:
Pr(A∪B) = Pr(A) + Pr(B) – Pr (A ∩ B)
Understand if mutually exclusive events, use
Pr(A∪B) = Pr(A) + Pr(B) because Pr(A∩ B)= 0
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Understand how conditional probability
reduces/changes the sample space and hence
the theoretical probability values
Learn and apply the rule which reads ’the
probability of A occurring given B has occurred’
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Define and apply the terms: trial, experiment, event,
sample space, outcome
Assign the correct probability values to impossible,
certain, likely, unlikely and equally likely events
Know that all probability values lie between and
include 0 and 1
Assign probabilities to outcomes and determine
probabilities of events
Calculate experimental probabilities using the
appropriate formula
Calculate theoretical probabilities using the
appropriate formula
Calculate long run proportion
Assign probabilities to outcomes and determine
probabilities of events when doing worded problems
Apply the concepts and symbols for sets, union,
intersection, complement, mutually exclusive events,
empty(null) set and universal set as applied to Venn
Diagrams, Karnaugh(Two-way) Tables and probability
calculations
Know that ∩ means ‘and’
Know that ∪ means ‘or’
Know that for mutually exclusive events, Pr(A∩ B)= 0
Know that for complementary events,
Pr(A’) = 1-Pr(A)
Draw a Venn diagram and use it to calculate
probabilities
Draw a Karnaugh Diagram and use it to calculate
probabilities
Apply Venn Diagrams and Karnaugh diagrams to
worded application problems
Apply the addition rule correctly to determine
probabilities for all types of events
Use the conditional probability rule accurately
Find conditional probabilities using a Venn diagram
or Karnaugh Diagram
Use the language of ‘if. .then’, ‘given that’ or ‘if’ to
investigate conditional statements and identify
common mistakes in interpreting such language
To know how to adjust this rule to certain
situations
10A Mathematics 2013 (SP&BMC)
1
Year 10A Mathematics
8.5 Multiple
events using
tables
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8.6 Using
tree
diagrams
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Chapter 8 Probability
Learn to use a table(lattice diagram) to
determine a sample space for multiple events
Learn the difference between assigning
probabilities for events involving selection
‘without replacement’ and ‘with replacement’
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Learn to use a tree diagram to determine a
sample space for multiple events
Use tree diagrams to show the difference
between assigning probabilities for events
‘without replacement’ and ‘with replacement’
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8.7
Independent
events
 Define independent events as the outcome of
one event not affecting the outcome of another
event
 Know that for independent events
Pr(A∩ B)=Pr(A) x Pr(B)
 Know that for independent events the
conditional probability formula becomes
Pr(A│B)= Pr(A)
 Know that independent events involve selection
without replacement
 Know that selection with replacement are not
independent events
 Learn and apply the addition rule to independent
events Pr(A∪B) = Pr(A) + Pr(B) – Pr(A) x Pr(B)
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Vocabulary
To be able to understand and use the following
mathematical terms:
 trial, experiment, event, sample space,
outcome, universal set, impossible, certain,
likely, unlikely and equally likely events, long run
proportion, experimental probability,
theoretical probability, intersection, union,
empty(Null) set, Venn diagrams, Karnaugh
diagrams (two-way tables), Lattice diagrams,
Tree diagrams, multiple events, independent
events, mutually exclusive events, conditional
probability, selection ‘with replacement’ and
selection ‘without replacement’
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10A Mathematics 2013 (SP&BMC)
Use a table( Lattice diagram) to determine a sample
space for multiple events
assign probabilities for events involving selection
‘without replacement’ and ‘with replacement’
Use a tree diagram to determine a sample space for
multiple events
Use a tree diagram to accurately assign probabilities
for events ‘without replacement’ and ‘with
replacement’
Use tree diagrams to accurately assign probabilities
and hence solve application problems
Use tree diagrams, Venn diagrams, Karnaugh
diagrams, the conditional probability rule and the
addition rule accurately to solve application problems
involving independent events
I can understand and use vocabulary related to
Probability and Venn Diagrams
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