Probability Revision 1-Problem Solving

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9th
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PROBABILITY REVISION 1

WORKSHEETS AND STEP-BY-STEP SOLUTIONS

Learning Outcomes:

• Venn diagrams and the addition theorem

• Multi-stage experiments and the product rule

• Mutually Exclusive Events

• Probability tree diagrams

• Conditional Probability

• Independent Events

Also comply with Australian Curriculum

Review the concepts and language of outcomes, sample spaces and events as sets of outcomes (ACMMM049)

Use set language and notation for events, including A` for the complement of an event A, A∩B for the intersection of events A and B, and AՍB for the union, and recognise mutually exclusive events (ACMMM050)
Use everyday occurrences to illustrate set descriptions and representations of events, and set operations. (ACMMM051)
Review probability as a measure of ‘the likelihood of occurrence’ of an event (ACMMM052)
Review the probability scale: 0 ≤ P(A) ≤1 for each event A, with P(A) = 0 if A is an impossibility and P(A) = 1 if A is a certain (ACMMM053)
Review the rules: P(A`) = 1 − P(A) and P(A∪B) = P(A) + P(B) − P(A∩B) (ACMMM054)
Use relative frequencies obtained from data as point estimates of probabilities. (ACMMM055)
Understand the notion of a conditional probability and recognise and use language that indicates conditionality (ACMMM056)
Use the notation P(A|B) and the formula P(A|B) = P(A∩B)/P(B) (ACMMM057)
Understand the notion of independence of an event A from an event B, as defined by P(A|B) = P(A) (ACMMM058)
Establish and use the formula P(A∩B) = P(A)P(B) for independent events A and B, and recognise the symmetry of independence (ACMMM059)
Use relative frequencies obtained from data as point estimates of conditional probabilities and as indications of possible independence of events. (ACMMM060)