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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 B. Theoretical Probability

Indicator 1. Determine the probability of an event comprised of no more than 2 independent events

Objective a. Express the probability of an event as a fraction, a decimal, or a percent

Assessment limit: Use a sample space of no more than 35 outcomes and decimals with no more than 2 decimal places

Clarification

Probability is the chance or likelihood of an event happening. The outcomes are all the possible results of an activity, either theoretical or experimental, that can occur. When rolling two number cubes, there are 36 possible sums of the cubes that can occur. Those 36 sums produce 11 unique results called the sample space of the activity. An event is a specific set of outcomes from the activity. When rolling two number cubes there are 6 possible sums of 7 that can occur. We talk about rolling a 7 as an event. An event composed of one single event is called a simple event. A simple event occurs when you roll one number cube and determine whether you get a 5. An event composed of more than one event occurring at the same time is called a compound event. A compound event occurs when you roll two number cubes to determine if the sum of the numbers shown on the cubes is 7.

Classroom Example 1

When rolling two number cubes, there are 36 sums (outcomes) of the numbers shown on the cubes. This is a compound event made up of two events, rolling cube 1 and rolling cube 2. The sample space for the sums of the numbers shown on the cubes when rolling two number cubes is {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}.

6x6 number cube

What is the probability of rolling a 7?

Answer:

According to the chart in which the possible outcomes are recorded, there are 6 different ways to roll a 7: 1+6, 2+5, 3+4, 4+3, 5+2, and 6+1. There is a 6/36 chance you will get a sum of 7 when you roll two number cubes. This may be thought of as 6 out of 36 chances.

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Classroom Example 2

What is the probability of rolling a sum greater than 10?

Answer:

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Classroom Example 3

Use the Fundamental Counting Principle to justify that there are 36 possible sums when rolling two number cubes.

Answer:

There are 6 possible ways number cube 1 can be rolled. There 6 possible ways number cube 2 can be rolled. According to the Fundamental Counting Principle, there are 6 • 6 or 36 combinations, or sums, of the numbers from cube 1 and cube 2.
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Resources for Objective 5.B.1.a:
CLARIFICATIONS | Sample Assessments |