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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 survey or simulation

Objective a. Make predictions and express the probability of the results as a fraction, a decimal with no more than 2 decimal places, or a percent

Assessment limit: Use results of 25 or 50

Clarification

Theoretical probability is the probability of an event occurring based on mathematical counting techniques. Under ideal conditions, theoretical probability describes what we expect to happen in the long run. Experimental probability is the estimated probability based on observations made during an experiment. 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.

Many times we can use the techniques of experimental probability to model a situation that may be difficult or even impossible to observe in real life by conducting a simulation. We can model these situations using common tools, such as number cubes, coins, or spinners or technology, such as calculators. We can also conduct a survey, in which people are asked questions whose responses are used to determine the probability of an event occurring. This is another example of the use of experimental probability.

Classroom Example 1

A spinner has eight equal sized sections shown below.

spinner image

Lois spins the spinner 25 times. The data below shows where the spinner stopped each time.

White Blue Red Yellow White
Brown Green Red Black Orange
Red Blue Orange Yellow Red
Brown White Black Brown Brown
Red Blue Yellow Red Blue

Luis spins the spinner 50 more times. Based on the experimental probability, what is the percent of times that the spinner will land on brown?

Answer: In order to answer this question, a student must know that the probability will be based on the chart (experiment) and not the theoretical probability. Probability is the number of favorable outcomes divided by the total number of possible outcomes. This can be represented as:

equation image

Since there are 25 original spins, there are 25 possible outcomes. Since there are 4 times that the spinner landed on brown, there are 4 favorable outcomes. Since the question asks for the answer as a percent the student must rewrite 4/25 as a percent: 4/25 = 16%. The answer is 16%.

Luis spins the spinner 50 more times. Based on the theoretical probability, what is the percent of times that the spinner will land on brown? Compare this answer to the experimental probability.

Answer: There are eight equal sized sections of the spinner. There is only one brown section. We would expect, theoretically, that Luis will land on the brown section 1 out of 8 times. 1/8 = 12 1/2% The experimental probability of landing on brown is larger than the theoretical probability.

Classroom Example 2

Jenn took a survey of 25 of her classmates to see who did their math homework last night. Below are the results of the survey.

Yes-all of it No-none of it Some of it
16 5 4

Based on the results, what percent of the students should the teacher expect to complete all of their homework tonight?

Answer: P(yes)= 16/25 = 64%

Classroom Example 3

Marla surveyed 30 students in her school and learned that 18 of those students play soccer. Based on her survey results, what is the probability that every student in her school plays soccer?

Answer: P(soccer)= 18/30 = 0.60 = 60 %.
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