Practice Experimental vs. Theoretical Probability in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

Theoretical probability is calculated from known outcomes (P = \frac{\text{favorable}}{\text{total}}), while experimental probability is estimated from actual trials (P \approx \frac{\text{times event occurred}}{\text{total trials}}). As the number of trials increases, experimental probability tends to approach theoretical probability.

Theoretical probability is what SHOULD happen in a perfect world: a fair coin should land heads 50\% of the time. Experimental probability is what ACTUALLY happens when you try it: flip a coin 20 times and you might get heads 12 times (60\%). The more times you flip, the closer your experimental result gets to 50\%—that's the law of large numbers in action.

Example 1

easy
A coin is flipped 20 times: 13 heads. Compare experimental probability of heads to theoretical probability. Explain why they differ and when they converge.

Example 2

medium
A thumbtack is tossed 200 times: 130 times it lands point-up. Calculate the experimental probability. Explain why we must use experimental (not theoretical) probability here.

Example 3

easy
A die is rolled 60 times. Theoretical expected count for each face: 10. Actual counts: 1→8, 2→11, 3→9, 4→12, 5→10, 6→10. Calculate experimental probability for rolling a 1 and compare to theoretical.

Example 4

hard
A 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.
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