In this Grade 7 lesson from Illustrative Mathematics Chapter 8, students learn how to identify and organize sample spaces for multi-step experiments using three methods: lists, tables, and tree diagrams. The lesson applies these strategies to real-world scenarios like choosing meals or clothing combinations, and introduces the multiplication principle to count total outcomes. Students then use sample spaces to calculate probabilities of specific outcomes in multi-step events.
Section 1
Creating Tree Diagrams for Compound Events
A tree diagram systematically displays all possible outcomes of compound events by creating branches for each outcome of the first event, then extending branches for each outcome of subsequent events from every existing branch.
Section 2
Probabilities of compound events
Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. 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.
A compound event is an event that can be viewed as two or more simpler events happening. If the simple events do not influence each other, they are called independent events. For independent events, the probability of the compound event is the product of the probabilities of the simple events.
A compound event combines two or more simple events. If they are independent (one does not affect the other), find the total probability by multiplying their individual probabilities. It is like a chain reaction of chances!
Section 3
Using Area Models for Probability
An area model, or table, can represent the sample space of a two-step experiment. The rows show the outcomes of the first event, and the columns show the outcomes of the second. Each cell represents one possible outcome in the sample space, and the total number of cells gives the total number of outcomes.
An area model is a grid used to visualize all possible outcomes of a multi-step experiment. It is especially useful for two-step events, like rolling two dice or flipping a coin twice. By counting the cells that match the desired event and dividing by the total number of cells, you can easily calculate the theoretical probability. This method provides a clear and organized alternative to a tree diagram or simple list.
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Section 1
Creating Tree Diagrams for Compound Events
A tree diagram systematically displays all possible outcomes of compound events by creating branches for each outcome of the first event, then extending branches for each outcome of subsequent events from every existing branch.
Section 2
Probabilities of compound events
Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. 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.
A compound event is an event that can be viewed as two or more simpler events happening. If the simple events do not influence each other, they are called independent events. For independent events, the probability of the compound event is the product of the probabilities of the simple events.
A compound event combines two or more simple events. If they are independent (one does not affect the other), find the total probability by multiplying their individual probabilities. It is like a chain reaction of chances!
Section 3
Using Area Models for Probability
An area model, or table, can represent the sample space of a two-step experiment. The rows show the outcomes of the first event, and the columns show the outcomes of the second. Each cell represents one possible outcome in the sample space, and the total number of cells gives the total number of outcomes.
An area model is a grid used to visualize all possible outcomes of a multi-step experiment. It is especially useful for two-step events, like rolling two dice or flipping a coin twice. By counting the cells that match the desired event and dividing by the total number of cells, you can easily calculate the theoretical probability. This method provides a clear and organized alternative to a tree diagram or simple list.
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter