Compute and compare theoretical and experimental probability in simple settings.
Compare theoretical and experimental probability
Problem
For a fair number cube labeled \(1~\text{through}~6\), calculate the theoretical probability of an even result. In \(24~\text{experimental}~\text{rolls}\), an even number occurred \(14~\text{times}\). Compare the theoretical and experimental probabilities.
Big Picture
What this problem is really about
Build the two probabilities from different evidence: equally likely cube faces for theory and observed even rolls for the experiment. Simplify both fractions, then rewrite them with a common denominator or as decimals before comparing. Matching forms makes the comparison fair and avoids treating raw counts from different totals as probabilities.
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