Multinomial Probability Calculator
Calculate the probability of one complete category-count vector using normalized entered category weights.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Normalize the weights and evaluate the multinomial coefficient and count powers in logarithmic form.
P(count vector)=n!/Πki! × Πpi^ki, with pi=weighti/Σweights
Worked example
Counts 2,1,1 and category probabilities 0.5,0.25,0.25 give probability 0.1875 for that unordered count vector.
Assumptions and input details
2–20 categories, matching lists and at most 10000 total observed counts. Counts sum to the modeled trial count. Zero-probability categories with positive counts give probability zero. No goodness-of-fit tail or parameter fitting.
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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