Ohio Resource Center
Lessons
Tree Diagrams and Probability
Discipline
Mathematics
6, 7, 8
Professional Commentary

This lesson is a step-by-step introduction to tree diagrams for computing probabilities of simple compound events. A Racing Game applet is included, along with discussion questions and suggestions for guided and independent practice. (sw)

Common Core State Standards for Mathematics
Statistics and Probability
Investigate chance processes and develop, use, and evaluate probability models.
7.SP.C.5
Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.
7.SP.C.7
Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.
1. Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected.
2. Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies?
7.SP.C.8
Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.
1. Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.
2. Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., “rolling double sixes”), identify the outcomes in the sample space which compose the event.
3. Design and use a simulation to generate frequencies for compound events. For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood?
Ohio Mathematics Academic Content Standards (2001)
Data Analysis and Probability Standard
Benchmarks (5–7)
I.
Describe the probability of an event using ratios, including fractional notation.
Benchmarks (8–10)
J.
Compute probabilities of compound events, independent events, and simple dependent events.