Understand and apply the concepts of probability to solve problems including those in real-life contexts Investigate and develop understanding of a variety of methods for counting possibilities including lists, tree diagrams, and grids Understand the concept of expected return in analyzing whether a game is fair or not
Conceptual Framework
logic justification, representation in the context of fairness and development
Statements of Inquiry
Understanding the logic behind probability allows us to make more informed and fair decisions
Factual
How can we quantify uncertainty?
How do we know if two events are independent?
Conceptual
How can we use probability to gain an advantage?
Debatable
To what extent is probability actually useful?
Can an understanding of probability enrich our lives?
Description
The fascinating study of probability takes a hands-on approach to develop students understand of theoretical probabilities as they arise from performing simple experiments over a large number of trials. The challenging logic behind probabilistic thinking has often led to raging controversies amongst top mathematicians the world over - the famous Monty Hall problem, just to name one. Students will learn various approaches to calculating the probabilities of two or more contiguous or mutually exclusive events and how conditional probability plays a role in justifying decisions that we make everyday.
Learning Outcomes
Understand the language and terminology associated with the study of probability - random experiment, outcome, sample space, event, distribution, relative frequency, probability,expected value, conditional probability
Develop understanding of impossible events, certain events
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 expected values
Understand the concept of a fair game and manipulate payouts to ensure that a game is fair