In this math video lesson we will learn about compound probability and tree diagrams. Our lesson objectives are - Students will determine the number of possible outcomes of compound events, Students will create organized lists, tables, & tree diagrams to represent compound probabilities, and Students will use tree diagrams to find the probability of compound events. Our Essential Question is - How can a tree diagram help you determine the probability of compound events? We will define sample space, outcome, tree diagram and compound probability. A sample space is a list of all possible outcomes for a chance experiment. An outcome is one of the things that can happen during an experiment. A tree diagram is a diagram that is used to organize the sample space of events. Compound Probability is the probability of two or more events happening. We will create a tree diagram that represents a sample space that represents a real world situation. We will identify a specific outcome in the sample space. We will use the tree diagram to determine the total number of possible outcomes. We will also learn about the Fundamental Counting Principle. The Fundamental Counting Principle is a way to figure out the total number of possible outcomes. To use the principle, multiply the number of ways for each event to find the total number of possible outcomes. I will model how to use this with a tree diagram, as well as a real world situation where a tree diagram is not practical. We will also represent a sample space as an organized list and using a table. We will use a tree diagram to find compound probabilities. Student practice is embedded in the lesson with modeled exemplar solutions.
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00:00 Introduction
00:11 Lesson Objectives
00:31 Essential Questions
00:50 Vocabulary - sample space, outcome, tree diagram & compound probability
01:34 How to Create a Tree Diagram
03:20 Identify an Outcome in a Tree Diagram
03:45 Total Possible Outcomes
05:22 The Fundamental Counting Principle
06:44 Using the Fundamental Counting Principle
08:50 Student Practice #1 - Fundamental Counting Principle
09:22 Solution - Student Practice #1
10:14 Student Practice #2 - Create a Sample Space
10:51 Three Ways to Create a Sample Space
11:34 How to Make an Organized List
12:08 How to Use a Table as a Sample Space
12:54 How to Find Compound Probability
14:27 Student Practice #3 - Compound Probability
14:52 Solution - Student Practice #3
15:25 Student Practice #4
15:55 Solution - Student Practice #4
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Statistics
Investigate chance processes and develop, use, and evaluate probability models.
7.SP.C.8 Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.
7.SP.C.8.a 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.
7.SP.C.8.b 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.
7.SP.C.8.c 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?