Investigate and apply the concepts of probability, counting principles, and solve problems including those set in real-life contexts Investigate the difference between theoretical probability and what happens in real life using a simulation Use a variety of strategies to calculate probabilities of one or multiple events, depending on the situation. Design and create a game comparing their theoretical probabilities with data they collect by playing the game
Conceptual Framework
Logic generalisation, representation in the context of Fairness and development
Statements of Inquiry
Understanding the logic behind probability allows us to make better decisions
Factual
How do we know if two events are independent?
What are the best diagrams to use to help us determine all the possible outcomes of an experiment?
Conceptual
How can we use probability to gain an advantage?
Debatable
Is logic ever wrong?
Is the world always certain and fair?
Description
This unit will focus on developing a range of strategies to calculate probabilities. The students will be exposed to the notation of probability, sample spaces, Venn Diagrams and Tree Diagrams. The students will also look at combinatorics in order to find the number of combinations that can occur when there is more than one event happening simultaneously. The students will also learn about conditional probability and expected values. The students will develop skills using excel to simulate multiple iterations of a random event. All of these skills will be used for the end of the unit task, in which the students will create their own game and determine whether or not their game is fair. The theoretical probabilities will be calculated for their game and then compared to the experimental data that they collect when the rest of the class play their game. A final report will be written and based on their findings.
Learning Outcomes
Master understanding of key terms including probability, outcome, event, impossible event, certain event, frequency, relative frequency, sample space
Understand the difference between experimental and theoretical probability
Use tree, lattice and Venn diagrams to solve probability problems
Calculate the probability of a single event as a fraction or decimal
Calculate the probability of combined and mutually exclusive events
Distinguish between and calculate the probability of independent and dependent events
Calculate the conditional probability of an event given that a previous event has occurred
Investigate and develop understanding of permutations and combinations for counting all possible outcomes of an experiment
Calculate expected values and interpret the expected value of a fair game
Understand the concept of a fair game and manipulate payouts to ensure that a game is fair.