Experimental vs. Theoretical Probability Math Example 4
Follow the full solution, then compare it with the other examples linked below.
Example 4
hardA simulation model predicts 25% of customers churn per month. After 6 months of actual data: 28%, 22%, 26%, 24%, 27%, 23%. Calculate the experimental mean, compare to theoretical, and determine if the model is reasonable.
Solution
- 1 Experimental mean: — matches theoretical exactly
- 2 Variation: monthly values range from 22% to 28% — natural random variation around 25%
- 3 Model assessment: the theoretical 25% is consistent with observed data; monthly fluctuations are noise around the signal (25%)
- 4 Conclusion: the model is reasonable — long-run experimental mean converges to theoretical prediction
Answer
Experimental mean = 25% = theoretical prediction. Monthly variation is noise; model is reasonable.
Comparing simulation predictions to real data validates the model. Small sample-to-sample variation is expected; the key is whether the long-run average matches. This is how modelers validate whether their theoretical probability assumptions match reality.
About Experimental vs. Theoretical Probability
Theoretical probability is calculated from known outcomes (), while experimental probability is estimated from actual trials (). As the number of trials increases, experimental probability tends to approach theoretical probability.
Learn more about Experimental vs. Theoretical Probability →More Experimental vs. Theoretical Probability Examples
Example 1 easy
A coin is flipped 20 times: 13 heads. Compare experimental probability of heads to theoretical proba
Example 2 mediumA thumbtack is tossed 200 times: 130 times it lands point-up. Calculate the experimental probability
Example 3 easyA die is rolled 60 times. Theoretical expected count for each face: 10. Actual counts: 1→8, 2→11, 3→