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Session 3 Study Guide: Experimental vs. Theoretical Probability

Data Science for Young Minds — Grade 3

Key Topics

TopicDetails
Theoretical probabilityTheoretical probability: calculated from math, not experiments
Why a fair coin should land heads 50% ofWhy a fair coin should land heads 50% of the time — in theory
Calculating theoretical probability for Calculating theoretical probability for dice, spinners, and cards
The key wordThe key word: 'should' — theory predicts the ideal, not the actual
Experimental probabilityExperimental probability: calculated from actual experiment results
How to calculateHow to calculate: number of times it happened / total trials
Why experimental results rarely match thWhy experimental results rarely match theoretical exactly
ActivityActivity: flip a coin 50 times and calculate experimental probability of heads
What the law of large numbers saysWhat the law of large numbers says: more trials = closer to theory
10 flips vs 100 flips vs 1000 flips10 flips vs 100 flips vs 1000 flips: watching convergence
Why this mattersWhy this matters: small samples are unreliable
ActivityActivity: flip a coin 10, 50, and 100 times — graph how the percentage changes
Small sample illusionsSmall sample illusions: patterns that are not real
The hot hand fallacy in sportsThe hot hand fallacy in sports
Why medical studies need thousands of paWhy medical studies need thousands of participants
How to recognize when a sample is too smHow to recognize when a sample is too small to trust

Lesson Summaries

Lesson 1: What Should Happen: Theoretical Probability

Calculate what should happen based on math alone — before running any experiment.

Lesson 2: What Actually Happens: Experimental Probability

Run experiments and see how results compare to theoretical predictions.

Lesson 3: The Law of Large Numbers

The more you repeat an experiment, the closer results get to the theoretical prediction. This is one of the most powerful ideas in probability.

Lesson 4: Why Small Samples Fool Us

Small groups of data can show dramatic patterns that disappear with more data. Learn why this matters for real-world decisions.

Review Questions

  1. What is theoretical probability?
  2. Why is it called 'theoretical'?
  3. How do you calculate theoretical probability?
  4. Does theoretical probability guarantee results?
  5. What is experimental probability?
  6. How is it different from theoretical?
  7. Why do experimental results vary?
  8. Is experimental probability wrong if it differs from theoretical?
  9. What is the law of large numbers?
  10. Why might 10 coin flips give 7 heads?
  11. How many trials is enough?
  12. Why does this matter for data science?
  13. What is a small sample illusion?
  14. What is the hot hand fallacy?
  15. Why do medical studies need large samples?
  16. How do you know if a sample is too small?