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Probability Models and Experimental Probability
Students build probability models and compare theoretical probability with long-run experimental results.
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Beginner
15–20 minutes
Probability & Statistics
Probability & Statistics
Page 5 of 8
Inside Cover
Probability Models and Experimental Probability
At a Glance
Binder SectionProbability & Statistics
DifficultyBeginner
Estimated Time15–20 minutes
PrerequisitesNone
How can simulation estimate probabilities that are difficult to calculate directly?
Build Understanding
Probability measures likelihood from 0 to 1. In an equally likely sample space, P(event) = favorable outcomes divided by total outcomes. The probabilities of all outcomes in a valid model sum to 1.
Theoretical probability comes from a model; experimental probability comes from observed trials. With many fair, independent trials, experimental results tend to approach the theoretical probability.
Visual Model
4Thousands
3Hundreds
2Tens
7Ones
4,327 = 4,000 + 300 + 20 + 7
Goals
Learning Targets
- 0 means impossible; 1 means certain.
- List the sample space carefully.
- P(not A) = 1 - P(A).
- Experimental probability = successes divided by trials.
- More trials usually stabilize relative frequency.
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Interactive Vocabulary
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Reveal one step at a time
Worked Examples
Example 1
Simulate three coin flips with random digits 0–4 as heads and 5–9 as tails.
1
Record whether at least two heads occur.
2
Repeat many trials.
Example 2
Worked Example 2
1
Compare simulated frequency with exact probability 4/8=1/2.
Ask and explain
Common Questions
Must all outcomes be equally likely? No; only use simple counting when they are.
Does a probability of one-half guarantee half the next ten trials? No.
Can experimental probability differ from theory? Yes, especially with few trials.
Notice and correct
Common Misconceptions
Using a simulation that does not preserve probabilities
Match each outcome to proportional random-number ranges.
Drawing a conclusion from too few trials
Increase trials and report variability.
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Warm-Up
Guided
Independent
Challenge
1
Quick Start
Warm-Up
A fair event has probability 0.30. Assign random digits 0–9.
2
We Do
Guided Practice
P(rolling a 4 on a fair die) = 1/6.
P(not rolling a 4) = 5/6.
18 successes in 30 trials gives experimental probability 3/5.
A spinner model is valid when sector probabilities total 1.
A larger number of trials generally gives a more stable estimate.
3
You Do
Independent Practice
A fair event has probability 0.30. Assign random digits 0–9.
Create and solve a second example with different values.
4
Stretch Your Thinking
Challenge & Real-World Practice
Design a valid simulation for a real multistage situation, run enough trials, and compare the estimate with an exact or reasoned benchmark.
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- I can identify the important information.
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Question 1
What should happen before calculating?
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Question 2
Which response gives the strongest evidence?
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Question 3
What is an effective accuracy check?
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Question 4
Why are units or labels important?
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What should a student do after finding an error?
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