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<p><strong>ADVANCED PROBABILITY QUESTION</strong><br /> about multi-stage event probability and step by step solution in two different ways (methods).</p> <p>Students think critically to solve the “Probability of Winning Both Games” question. This challenge question requires students to use their knowledge &amp; understanding of probability concepts and to come up with mathematical strategies to solve the problem.</p> <p><strong>Learning Outcomes:</strong></p> <p>• Use arrays or tree diagrams to determine the outcomes and the probabilities for multi-stage events.</p> <p>• Understand events using the language of ‘equally likely’, ‘at least’, etc.</p> <p>• Use complementary event to determine the probabilities associated with simple games.</p> <p>• Use &amp; solve a quadratic equation form that related to the probability of multi-stage events.</p> <p><strong>Also comply with Australian Curriculum</strong></p> <p>Identify complementary events and use the sum of probabilities to solve problems (ACMSP204)</p> <p>Describe events using language of ‘at least’, exclusive ‘or’ (A or B but not both), inclusive ‘or’ (A or B or both) and ‘and’. (ACMSP205)</p> <p>Describe the results of two- and three-step chance experiments, both with and without replacement, assign probabilities to outcomes and determine probabilities of events. Investigate the concept of independence (ACMSP246)</p> <p>Simple probabilities: construct a sample space for an experiment (ACMEM154)</p> <p>Use a sample space to determine the probability of outcomes for an experiment (ACMEM155)</p> <p>Use arrays or tree diagrams to determine the outcomes and the probabilities for experiments. (ACMEM156)</p> <p>Probability applications: determine the probabilities associated with simple games (ACMEM157)</p> <p><a href="/resources/search/?q=probability%20castakeonmaths">Probability</a></p>

<p>**PROBABILITY REVISION 1</p> <p>WORKSHEETS AND STEP-BY-STEP SOLUTIONS**</p> <p>Learning Outcomes:</p> <p>• Venn diagrams and the addition theorem</p> <p>• Multi-stage experiments and the product rule</p> <p>• Mutually Exclusive Events</p> <p>• Probability tree diagrams</p> <p>• Conditional Probability</p> <p>• Independent Events</p> <p>Also comply with Australian Curriculum</p> <ul> <li> <p>Review the concepts and language of outcomes, sample spaces and events as sets of outcomes (ACMMM049)</p> </li> <li> <p>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)</p> </li> <li> <p>Use everyday occurrences to illustrate set descriptions and representations of events, and set operations. (ACMMM051)</p> </li> <li> <p>Review probability as a measure of ‘the likelihood of occurrence’ of an event (ACMMM052)</p> </li> <li> <p>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)</p> </li> <li> <p>Review the rules: P(A`) = 1 − P(A) and P(A∪B) = P(A) + P(B) − P(A∩B) (ACMMM054)</p> </li> <li> <p>Use relative frequencies obtained from data as point estimates of probabilities. (ACMMM055)</p> </li> <li> <p>Understand the notion of a conditional probability and recognise and use language that indicates conditionality (ACMMM056)</p> </li> <li> <p>Use the notation P(A|B) and the formula P(A|B) = P(A∩B)/P(B) (ACMMM057)<br /> Understand the notion of independence of an event A from an event B, as defined by P(A|B) = P(A) (ACMMM058)</p> </li> <li> <p>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)</p> </li> <li> <p>Use relative frequencies obtained from data as point estimates of conditional probabilities and as indications of possible independence of events. (ACMMM060)</p> </li> </ul>

<p><strong>PROBABILITY REVISION 2</strong></p> <p><strong>WORKSHEETS AND STEP-BY-STEP SOLUTIONS</strong></p> <p><strong>Learning Outcomes:</strong></p> <p>• Venn diagrams and the addition theorem</p> <p>• Multi-stage experiments and the product rule</p> <p>• Mutually Exclusive Events</p> <p>• Probability tree diagrams</p> <p>• Complementary Events</p> <p><strong>Also comply with Australian Curriculum</strong></p> <ul> <li>Review the concepts and language of outcomes, sample spaces and events as sets of outcomes (ACMMM049)</li> <li>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)</li> <li>Use everyday occurrences to illustrate set descriptions and representations of events, and set operations. (ACMMM051)</li> <li>Review probability as a measure of ‘the likelihood of occurrence’ of an event (ACMMM052)</li> <li>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)</li> <li>Review the rules: P(A`) = 1 − P(A) and P(A∪B) = P(A) + P(B) − P(A∩B) (ACMMM054)</li> </ul>