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# 6-D-2-2

last edited by 2 years, 6 months ago

6.D.2.2  Determine the sample space for a given experiment and determine which members of the sample space are related to certain events. Sample space may be determined by the use of tree diagrams, tables or pictorial representations.

In a Nutshell

A sample space is the set of all possible outcomes for a given probability experiment. For example, the sample space for the experiment of rolling a standard 6-sided die is {1,2,3,4,5,6}. Tree diagrams, tables, and pictorial representations can be used to organize all possible outcomes to determine the sample space of an experiment that involves more than one action, such as rolling a die and then flipping a coin. These representations can also be used to identify subsets of the sample space which are outcomes related to certain events of an experiment like the outcomes for rolling an even number on the die and getting tails in the experiment mentioned above.

## Teacher Actions

• Develop strategies for problem solving by using multiple representations like tree diagrams, tables, and pictures as a strategy to determine the sample space for a given experiment and which members of the sample space are related to certain events.

• Develop the ability to communicate mathematically through writing and discussion about the various strategies for determining and representing the sample space of a given experiment and determining which members of the sample space are related to certain events.

• Use and connect mathematical representations for sample spaces like tree diagrams, tables, and pictures by modeling the various strategies to represent the set of all possible outcomes of a given experiment and engaging students in making connections between these representations to deepen their understanding of sample space. Below is an example of a tree diagram for the experiment that involves tossing a 2-sided coin three times. • Pose purposeful questions to assess and advance the students’ reasoning and sense making about sample space.  For example, when making the sample space for the experiment of rolling two dice, the teacher could ask “Should the outcome of rolling a 2 and 1 (2,1) be included in the sample space if you already have (1, 2) in the sample space?”

• Implement tasks that promote reasoning and problem solving involving real-world applications of samples space such as selecting an outfit for school.

## Misconceptions

•  Understand the sample space is the set of all possible outcomes for a given probability experiment

• Understand the sample space of an experiment can be determined using tree diagrams, tables, and pictorial representations.

• Understand the outcomes in an event for a given experiment are a subset of the experiment’s sample space.

• Not include all possible outcomes in a sample space.  For example, when rolling two dice, students may leave out the outcome of rolling a two and 1 (2,1) because they already have (1,2) in the sample space.  They do not recognize that these two outcomes are different and both should be included in the sample space.

OKMath Framework Introduction