School Improvement in Maryland
Calculating Theoretical & Experimental Probability
Data Analysis and Probability .

  • Students will collect data by conducting a survey of fellow classmates.
  • Students will investigate the relationship between estimates obtained from samples and theoretical probabilities.
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Core Learning Goals
  • 3.1.3: The student will calculate theoretical probability or use simulations or statistical inferences from data to estimate the probability of an event.
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  • A random sample of 150 people are asked if they own dogs, and 57 of them say yes. What would you estimate the percentage of dog owners to be in the general population?
    (The sample proportion is 57/150=0.38. Since the sample is random, the percentage of the population owning dogs should be close to 38%.)
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  • Activities: "Collecting Your Own Data," "From the Experimental to the Theoretical," and "Calculating Theoretical Probabilities"
  • Answer Keys
  • Coins, dice, spinners, or other similar devices
  • .  Print Version: (Acrobat 47k)
    The print version contains all student worksheets and answer keys needed to complete the lesson.

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Calculator Skills
  • NONE
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  • Drill. Students will estimate the population percentage from the results of a sample survey.
  • Exploration. The first activity, "Collecting Your Own Data," helps students grasp how survey results can be used to make predictions regarding the population. The activity also gives students experience with experimental probability. The next activity relates probabilities determined from sample results to those that we would expect in the long run by combining all possible samples. In "From the Experimental to the Theoretical" it may be necessary to combine students' results to show that experimental probabilities will approach the theoretical values in the long run or after many tosses.
  • Class Discussion. Students need to understand that experimental probabilities vary because they depend on the results of samples. However, theoretical probabilities are determined by considering all possible outcomes and how often they occur in the long run. For example, the theoretical probability of tossing a coin and landing on heads is 50%. This value means that it the long run, after many, many tosses, we can expect a coin to land on heads approximately half the time. It does not mean that the coin will land on heads once in two tosses.
  • Additional problems. The last activity gives students practice calculating theoretical probabilities.
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  • Summary Questions:
    Randy wanted to determine his chances of making a basket in a basketball game. In 15 free throw attempts he made 9 of the shots.
    1. What proportion of shots did Randy make?
      (sample proportion: 9/15=0.60 )
    2. Do you think that this value is a good estimate for Randy's probability of making a basket? Use mathematics to justify your answer.
      (It is difficult to tell whether or not 0.60 is a good estimate because Randy attempted only 15 free throws. If he had attempted 1500 free throws and made 900 of them, we could be more confident in the estimate.)
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  • "Calculating Theoretical Probabilities"
Objective Objective Core Learning Goals Core Learning Goals Drill Drill Materials Materials Calculator Skills Calculator Skills Activities Activities Assessment Assessment Homework Homework