Advanced Probability - The Probability of Winning Both Games

ADVANCED PROBABILITY QUESTION
about multi-stage event probability and step by step solution in two different ways (methods).

Students think critically to solve the “Probability of Winning Both Games” question. This challenge question requires students to use their knowledge & understanding of probability concepts and to come up with mathematical strategies to solve the problem.

Learning Outcomes:

• Use arrays or tree diagrams to determine the outcomes and the probabilities for multi-stage events.

• Understand events using the language of ‘equally likely’, ‘at least’, etc.

• Use complementary event to determine the probabilities associated with simple games.

• Use & solve a quadratic equation form that related to the probability of multi-stage events.

Also comply with Australian Curriculum

Identify complementary events and use the sum of probabilities to solve problems (ACMSP204)

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)

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)

Simple probabilities: construct a sample space for an experiment (ACMEM154)

Use a sample space to determine the probability of outcomes for an experiment (ACMEM155)

Use arrays or tree diagrams to determine the outcomes and the probabilities for experiments. (ACMEM156)

Probability applications: determine the probabilities associated with simple games (ACMEM157)

Probability