Probability Revision 1-Problem Solving

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

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)