Experimental vs. Theoretical Probability Math Example 3

Follow the full solution, then compare it with the other examples linked below.

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.

Solution

  1. 1
    Experimental P(1)=8/60≈0.133P(1) = 8/60 \approx 0.133
  2. 2
    Theoretical P(1)=1/6≈0.167P(1) = 1/6 \approx 0.167
  3. 3
    Difference: 0.167−0.133=0.0340.167 - 0.133 = 0.034 — small discrepancy expected from random variation with only 60 trials

Answer

Experimental P(1) ≈ 0.133 vs. theoretical 0.167. Small difference consistent with random variation.
In any finite experiment, experimental probabilities will deviate from theoretical ones. These deviations are expected and quantified by the chi-square test. With more trials, experimental values converge to theoretical.

About Experimental vs. Theoretical Probability

Theoretical probability is calculated from known outcomes (P=favorabletotalP = \frac{\text{favorable}}{\text{total}}), while experimental probability is estimated from actual trials (P≈times event occurredtotal trialsP \approx \frac{\text{times event occurred}}{\text{total 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 medium

A thumbtack is tossed 200 times: 130 times it lands point-up. Calculate the experimental probability

Example 4 hard

A simulation model predicts 25% of customers churn per month. After 6 months of actual data: 28%, 22

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