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# Compound Probability

Use this math lesson to introduce compound events! Students will build on their understanding of probability as they learn how to find the sample space and probability of compound events given real-world examples.
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Use this math lesson to introduce probability of compound events! Building off students’ understanding of simple events, teachers will help students understand how to find the sample space of compound events and how to find the probability of compound events. To demonstrate understanding, students will find sample spaces of compound events and probabilities of compound events given real-world examples, partner work, and independent practice.

• Students will be able to determine the sample spaces of compound events.
• Students will be able to calculate compound probabilities.
(5 minutes)
• Prior to teaching this lesson, make sure you have introduced how to find simple probabilities to your students. Students should know the terms outcomes, events, and sample space.
• Put three different pieces of candy in a container, and show students the container. Ask students to independently find the probability of randomly selecting one specific piece of candy and write that probability on a sheet of paper.
• Show students a six-sided die. Ask students to independently find the probability of rolling a 5 and write that probability on the sheet of paper.
• Ask students to share their answers.
(10 minutes)
• Tell students that the probabilities they found in the Introduction are called simple probabilities. Note that each of those events by themselves are called simple events. Explain that in today's lesson, students will be finding compound probabilities.
• Define compound probability as the probability of a combination of two or more simple events. Tell students that when we combine two or more simple events, we get compound events. Explain that randomly selecting a piece of candy from a container and rolling a die together are compound events.
• Remind students of the ratio they use to find simple probability: the number of favorable outcomes over the number of outcomes in the sample space. Tell students they can use the same process for finding probabilities of compound events.
• Model how to find the sample space for selecting a candy from the container and rolling a die. Show this using a table, a tree diagram, and an organized list. Emphasize that each method shows the same sample space with 18 possible outcomes.
• Explain that once you've listed the events in the sample space, you can find the probability of a specific outcome. Model how to find the probability of randomly selecting a specific piece of candy from the container and rolling a 5 on the die.
• Direct students to turn to a partner and find some more compound probabilities: randomly selecting one piece of candy and then rolling a 3, randomly selecting another piece of candy and rolling a 1, and randomly selecting a third piece of candy and rolling a number greater than 4. Come back together and have students model how to find each probability.
(10 minutes)
• Hand out the Sample Spaces of Compound Events worksheet to your students.
• Have students work with their partners to complete this worksheet. Monitor students’ progress as they complete the worksheet.
(20 minutes)
• Hand out the Probabilities of Compound Events worksheet to your students.
• Have students work independently on these problems while you monitor student progress.
• After 15 minutes, ask students which problems were most challenging. Go over answers for those problems with the class.

Support:

• Provide manipulatives (e.g., die, coin) to struggling students to help them create the sample spaces.
• Provide highlighters or markers to struggling students so that they can highlight favorable outcomes on their lists, tree diagrams, and/or tables on the Probabilities of Compound Events worksheet.
• If students are struggling to solve the Probabilities of Compound Events worksheet independently, have them complete the problems with a partner.

Enrichment:

• If students finish the Probabilities of Compound Events worksheet early, challenge them to come up with a method for determining the number of outcomes in the sample space of compound events without using a list, table, or tree diagram. Encourage students to look at the sample spaces on the worksheets they've completed and try their method on those problems.
• Have students create their own compound probability problems. Challenge students to create compound events by combining three simple events.
(10 minutes)
• Show students a container with four different pieces of candy in it and a container with strips of paper labeled A, B, C, and D in it.
• Ask students to find the sample space of selecting a candy from the first container and selecting a letter from the second container. Ask students to also write the number of outcomes in the sample space.
• Ask for the probability of randomly selecting a specific piece of candy and randomly selecting a specific letter. Students should write their answers to this problem on the same sheet of paper.
• Collect this assessment to gauge student understanding from this lesson.
(5 minutes)
• After you have collected the assessments, have a student explain how they found the number of outcomes in the sample space and the probability for the assessment problems.

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