How this calculator works
Divide each count by the sum of all counts, then divide numerator and denominator by their greatest common divisor. The reduced fraction remains exact even when the displayed decimal repeats. Cumulative fractions follow the entered order and end at one. The input limits keep all integer totals within exact JavaScript integer range. Counts model theoretical probability only when elementary outcomes are equally likely; for observed data, the fractions are relative frequencies.
Formula
Probability = favourable/total. Reduced fraction = (favourable/g)/(total/g), where g = gcd(favourable,total). Complement = (total - favourable)/total.
Worked example
Outcome counts 2, 3 and 5 total 10. Their reduced probabilities are 1/5, 3/10 and 1/2. Their cumulative fractions are 1/5, 1/2 and 1/1. A separate event with 6 favourable outcomes out of 15 reduces to 2/5.
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Frequently asked questions
Why not convert the displayed percentage back into a fraction?
A rounded percentage can lose information. Reducing the original whole counts preserves the exact ratio.
Is a zero-count outcome valid?
Yes. Its reduced probability is 0/1. An all-zero list has no probability distribution and is rejected.
Can outcomes overlap?
Table mode assumes a complete list of non-overlapping categories. Overlapping event counts would count some elementary outcomes twice.
Does the cumulative probability depend on order?
Yes. Each cumulative fraction includes that row and every earlier row. Individual outcome probabilities do not change when the rows are reordered.