Overview
This lecture introduces the foundational concept of probability, distinguishes between theoretical and empirical probability, and explains why these ideas are essential for further study in statistics.
What is Probability?
- Probability measures the proportion or percentage of times a random event occurs.
- A random event is unbiased and unaffected by prior events.
- Randomness assumes no influence or pattern in the occurrence of events.
Types of Probability
- Theoretical probability is determined purely by mathematical reasoning, without conducting experiments.
- Example: Probability of heads in a coin toss is 1 out of 2 sides, or 50%.
- Example: Probability of drawing a Queen from a deck is 4 out of 52 cards.
- Empirical probability is determined by actual experiments, sampling, or observed data.
- Example: Flipping a coin 25 times and getting heads 11 times results in empirical probability of 11/25 or 44%.
- Empirical probability is often used when theoretical calculation is impractical (e.g., weather forecasts, election predictions, business success rates).
Comparing Theoretical and Empirical Probability
- Theoretical probability is seen as the "true" probability, based on all possible outcomes.
- Empirical probability is often a "short-term" proportion, derived from sample results.
- With more trials, empirical probability tends to approach theoretical probability.
Identifying Probability Types: Examples
- Claiming a 1/8 chance of three tails in a row is theoretical probability (uses math, no experiments).
- Reporting 10 fatalities in 31 million flights is empirical probability (based on collected sample data).
Importance and Next Steps
- Distinguishing between empirical and theoretical probability is crucial for statistical analysis.
- Statistics relies on empirical probability but aims to estimate the underlying theoretical probability.
- Future lessons will focus on calculating probabilities and connecting empirical results to theoretical expectations.
Key Terms & Definitions
- Probability — the proportion or percent of times a random event occurs.
- Random Event — an event with no bias, equally likely outcomes.
- Theoretical Probability — probability calculated using mathematical logic and all possible outcomes, without experiments.
- Empirical Probability — probability based on actual experiments, samples, or observed data.
Action Items / Next Steps
- Review definitions and examples of theoretical and empirical probability.
- Practice classifying scenarios as empirical or theoretical probability.
- Prepare to learn the mathematical methods for finding and comparing probabilities in upcoming chapters.