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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 a sample space

Objective a. Determine the number of outcomes

Assessment limit: Use no more than 3 independent events with a sample space of no more than 6 outcomes in each event.

Clarification

Probability is the chance or likelihood of an event happening. Each of the possible results of an activity, either theoretical or experimental, is an outcome. A set of all possible outcomes of an experiment is called a sample space. An event is a specific set of outcomes from the sample space. Two or more events are said to be independent events when the result of one event does not affect the outcomes of the other events. Two or more events are said to be dependent events when the result of one event does affect the outcomes of the other events.

Classroom Example 1

What is the total number of outcomes for the two spinners shown below?

two spinners image

This question can be solved using one of several methods shown below.

Method 1

Make a list of all possible outcomes for each spinner

1, A 2, A 3, A 4, A
1, B 2, B 3, B 4, B
1, C 2, C 3, C 4, C

Answer: 12 possible outcomes

 

Method 2

Make a tree diagram showing each possibility

tree diagram

Trace each path on the tree diagram to show all of the possible outcomes.

1, A 1, B 1, C
2, A 2, B 2, C
3, A 3, B 3, C
4, A 4, B 4, C

Answer: 12 possible outcomes

 

Method 3

Apply the Fundamental Counting Principle

Fundamental Counting Principle:

If one event can occur in m ways and a second event can occur in n ways, then the first event followed by the second event can occur in m • n ways.

The first spinner has 4 (m) possible outcomes (1, 2, 3, or 4). The second spinner has 3 (n) possible outcomes (A, B, or C). To determine the total number of possible outcomes for both independent events, multiply the number of outcomes for each event.

4•3 = 12

Answer: 12 possible outcomes
/instruction/clarification/mathematics/grade7/xml/5A1a.xml
Resources for Objective 5.A.1.a:
CLARIFICATIONS | Sample Assessments |