Calculated Result
This section stays above the form and updates after every submission.
| Joint Table | Col X | Col Y | Col Z | Row Total | Row Marginal Probability |
|---|---|---|---|---|---|
| Row A | 18.0000 | 12.0000 | 10.0000 | 40.0000 | 0.4000 |
| Row B | 15.0000 | 20.0000 | 5.0000 | 40.0000 | 0.4000 |
| Row C | 7.0000 | 9.0000 | 4.0000 | 20.0000 | 0.2000 |
| Column Total | 40.0000 | 41.0000 | 19.0000 | 100.0000 | - |
| Column Marginal Probability | 0.4000 | 0.4100 | 0.1900 | - | - |
Marginal Probability Graph
Calculator Form
Enter counts or joint probabilities. The calculator supports a complete 3×3 joint table.
Example Data Table
This example uses counts in a 3×3 joint table. Marginal probabilities come from row totals and column totals divided by the grand total.
| Example Table | Morning | Afternoon | Evening | Row Total |
|---|---|---|---|---|
| Group A | 8 | 6 | 4 | 18 |
| Group B | 5 | 9 | 3 | 17 |
| Group C | 7 | 2 | 6 | 15 |
| Column Total | 20 | 17 | 13 | 50 |
Sample marginal probabilities: P(Group A) = 18 / 50 = 0.36 and P(Afternoon) = 17 / 50 = 0.34.
Formula Used
Marginal probability is found by summing joint values across one variable and keeping the other variable fixed.
| From joint probabilities | P(X = xi) = Σ P(X = xi, Y = yj) |
|---|---|
| Column marginal | P(Y = yj) = Σ P(X = xi, Y = yj) |
| From counts | P(X = xi) = Row Total / Grand Total |
| From counts | P(Y = yj) = Column Total / Grand Total |
When the entered probabilities do not sum to 1, this calculator normalizes them before computing marginals.
How to Use This Calculator
- Choose whether your table contains counts or already contains joint probabilities.
- Rename the three row categories and three column categories to match your dataset.
- Enter the nine joint cells in the 3×3 matrix.
- Select one row and one column to highlight their marginal probabilities.
- Click Calculate Marginals to show the result section above the form.
- Review the table totals, marginal probabilities, and the grouped Plotly chart.
- Use the CSV or PDF buttons to export a clean report.
FAQs
1. What is marginal probability?
Marginal probability shows the probability of one event without conditioning on the other variable. You get it by summing across the relevant row or column.
2. What is the difference between joint and marginal probability?
Joint probability measures two events together in one cell. Marginal probability collapses one variable and keeps only the total probability for a row or column.
3. Can I enter frequencies instead of probabilities?
Yes. Choose the count mode. The calculator will divide row totals and column totals by the grand total to produce marginal probabilities.
4. Why do row and column totals matter?
Marginal probabilities come directly from those totals. Each row total measures one row category. Each column total measures one column category.
5. Why were my probabilities normalized automatically?
Joint probabilities should sum to 1. If your entries sum to a different value, the calculator rescales them so the resulting marginal probabilities remain valid.
6. Is this calculator limited to a 3×3 table?
This version is designed as a complete 3×3 calculator for clean layout and faster use. You can expand the matrix later if your project needs more categories.
7. What does the highest joint cell tell me?
It identifies the strongest combined row-column outcome in your table. That helps you spot the most common pairing before examining the marginals.
8. Where is marginal probability used in maths?
It is used in probability, statistics, machine learning, survey analysis, quality control, and decision models whenever two variables are summarized in one joint table.