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Clarifications: Each clarification provides an explanation of the indicator/objective to help teachers better understand the concept. Classroom examples are often included to further illustrate the concept. While classroom examples could be shared with the students, the intended audience for the explanation/clarification is the classroom teacher-not the student. In addition, classroom examples may or may not reflect the assessment limits.

Standard 5.0 Knowledge of Probability

Topic A. Sample Space

Indicator 1. Identify possible outcomes

Objective a. Determine possible outcomes of independent events

Assessment limit: Use two independent events with no more than 4 outcomes each and an organized list or tree diagram

Clarification

Two different methods can be used to find the total number of outcomes for independent events. One is a tree diagram and the other is an organized list. A tree diagram is constructed with branches that represent the outcomes of each independent event. The first set of branches lead to the outcomes of the first event and the next set of branches lead to the outcomes of the next independent event. To list the outcomes, read across each set of branches. An organized list is a systematic arrangement of outcomes. To complete the list, begin with the first outcome of the first independent event and arrange each of the outcomes of the next independent event with that first outcome. Then, select the second outcome of the first independent event and arrange the outcomes of the next independent event with that second outcome. Complete the process until all the outcomes are from the two events are arranged.

Classroom Example 1

Find the different kinds of ice cream dishes you can make with 2 types of ice cream (first independent event) and 4 toppings (second independent event).

Use a tree diagram to find the different combinations.

  • Begin with the first set of branches that represent the 2 types of ice cream.

    tree diagram

  • Continue by adding the next set of branches.

    tree diagram

  • Read across each set of branches to list the outcomes.

    chart

Classroom Example 2

Suppose you have 3 shirts and 3 pairs of pants. What are the different outfits you could make with the shirts (first independent event) and pants (second independent event)? Use an organized list to find the different outfits.

chart
/instruction/clarification/mathematics/grade5/xml/5A1a.xml
Resources for Objective 5.A.1.a:
CLARIFICATIONS | Thinking Skills | Sample Assessments |