Header for Calculating Probabilities Using a Tree Diagram
The approach of Modelling with Probability is to start from solving problems using the tree diagram as a tool. To start with, students use it to record the results of experiments so that they can use their data to analyse a problem.
For many students, using tree diagrams (and 2-way tables) with whole numbers (natural frequencies, rather than probabilities) will be all they need to enable them to understand how to decide between different courses of action.
However, students who want to move onto more advanced mathematical study will need to learn how to work with probabilities expressed as fractions. They will need to learn how to use a tree diagram with probabilities to analyse a problem, and in particular they need to learn when to multiply and when to add.
This collection of problems will help students to move from using a tree diagram as a means of representing data to using it as a means to structure a solution to a problem. They also provide scaffolding to help them understand why we multiply probabilities of independent events to get the probability of the combined event (along the branches of a tree) and why we add the probabilities of
the separate narratives which the different sets of branches represent.
Teachers should start with the article Calculating with tree diagrams which describes the process by which we envisage students making this transition.