What is Experimental Probability?
Experimental probability (also called empirical probability) is the probability determined by actually performing an experiment and recording the results. It is based on observed data, not theoretical calculations.
Theoretical vs. Experimental Probability:
| Aspect | Theoretical Probability | Experimental Probability |
|---|---|---|
| **Calculation** | Favorable outcomes / Total possible outcomes | Observed frequency / Total trials |
| **Accuracy** | Exact, fixed value | Approximate, changes with trials |
| **Example** | P(heads) = 1/2 | After 100 flips, 48 heads → 0.48 |
Formula for Experimental Probability:
\[
P(\text{Event}) = \frac{\text{Number of times event occurred}}{\text{Total number of trials}}
\]
Law of Large Numbers:
As the number of trials increases, the experimental probability gets closer to the theoretical probability.
Why Use Experimental Probability?
- When theoretical probability is unknown or difficult to calculate
- To test if a game or process is fair
- In real-world situations where outcomes are not equally likely
Steps to Find Experimental Probability:
- Perform the experiment many times (trials)
- Count how many times the event occurs
- Divide the count by the total number of trials