9651 /www/nrich/html/content/id/9651/ 10 0000-00-00T00:00:00 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0">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.<br></br> <br></br> 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.<br></br> <br></br> 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.<br></br> <br></br> 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.<br></br> <br></br> Teachers should start with the article <a href="http://nrich.maths.org/9648"><em>Calculating with tree diagrams</em></a> which describes the process by which we envisage students making this transition.  </mdoxml> 0 0 0 0 0 1 0