Experimental vs. Theoretical Probability

🔑 Key Concepts

  • Theoretical probability is the probability based on equally likely outcomes.
  • Experimental probability is based on actual results collected during an experiment.
  • Experimental results may differ from theoretical results.
  • The more trials performed, the closer experimental probability often gets to theoretical probability.
  • Tables and simulations can help compare expected and actual outcomes.

✏️ Worked Examples

🧠 Math Vocabulary

  • Probability: The likelihood that an event will occur.
  • Theoretical Probability: The probability based on reasoning and equally likely outcomes.
  • Experimental Probability: The probability based on collected data from an experiment.
  • Outcome: A possible result of an experiment.
  • Trial: One repetition of an experiment.

💡 Main Idea

Theoretical probability tells what should happen, while experimental probability tells what actually happened. Comparing the two helps students understand variation in real-world probability experiments.

📚 What You Should Already Know

Students should be comfortable working with fractions, basic probability, and interpreting tables.

🚀 What Comes Next

Students can extend these ideas by comparing larger sample sizes and investigating how simulations approach theoretical probability over time.