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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 C. Experimental Probability

Indicator 1. Analyze the results of a probability experiment

Objective a. Make predictions and express the experimental probability as a fraction, a decimal, or a percent

Assessment limit: Use no more than 30 results in the sample space

Clarification

Experimental probability is the estimated probability based on the observed number of times (frequency) an event occurs. Many times the theoretical probability of the occurrence of an event cannot be obtained and we then must rely on this observed estimated probability to make predictions. Even when the theoretical probability can be obtained, it is important that we understand that the experimental probability of an event approaches that of the theoretical probability of the event as the number of trials (observations) in the experiment increases.

Classroom Example 1

Luis has 10 cards lettered A through J with one letter on each card. Luis shuffles the cards and picks one card without looking. He replaces the card, shuffles the cards, and picks again. Luis does this 30 times. The data below shows which card Luis picked each time.

B C F G D A
C J H J I C
D F G E D F
A F D J G H
I E F F G H

What is the experimental probability of drawing a card lettered F?

Answer: The correct answer can be expressed in equivalent forms:

6/30 2/10 20/100 20% 0.2 0.20
 

What is the theoretical probability of drawing a card lettered F?

Answer: The correct answer can be expressed in equivalent forms:

1/10 10/100 10% 0.1 0.10
 

Compare the experimental probability of drawing a card labeled F to the theoretical probability of drawing a card labeled F. Which is larger? Why do you think that is true?

Answer: The experimental probability is larger. Students should explain that the number of trials is small. As the number of trials gets larger, the theoretical probability should be close in value to the experimental probability.
 

Predict the number of times you should draw a card lettered F in 100 draws.

Answer: 10
The prediction should be based on the theoretical probability, no matter how many times cards marked with the letter F have been drawn previously. The cards have no memory of prior draws.
/instruction/clarification/mathematics/grade6/xml/5C1a.xml
Resources for Objective 5.C.1.a:
CLARIFICATIONS | Sample Assessments |