Probability table calculator form
Enter four joint cells as counts or probabilities, then compute marginals, conditionals, unions, dependence metrics, and exports.
Example data table
This worked example starts with observed counts and converts them into a full probability table for quick checking.
| Joint outcome | Count | Probability |
|---|---|---|
| A and B | 18 | 0.3000 |
| A and Not B | 12 | 0.2000 |
| Not A and B | 10 | 0.1667 |
| Not A and Not B | 20 | 0.3333 |
| Total | 60 | 1.0000 |
From this table, P(A) = 0.5000, P(B) = 0.4667, P(A | B) = 0.6429, and P(A ∪ B) = 0.6667.
Formula used
- Joint probability: P(A ∩ B) = n(A ∩ B) / N when counts are provided.
- Marginal probabilities: P(A) = P(A ∩ B) + P(A ∩ Not B), and similarly for B.
- Conditional probability: P(A | B) = P(A ∩ B) / P(B), provided P(B) is not zero.
- Union rule: P(A ∪ B) = P(A) + P(B) − P(A ∩ B).
- Independence rule: A and B are independent when P(A ∩ B) = P(A) × P(B).
- Expected count: Eij = (row total × column total) / N for each cell.
- Chi-square check: χ² = Σ (O − E)² / E across the four cells when counts are used.
- Association strength: Phi coefficient and odds ratio summarize how strongly the two events move together.
How to use this calculator
- Choose whether your four inputs represent observed counts or finished probabilities.
- Rename Event A and Event B if you want domain-specific labels.
- Enter all four joint cells for the 2 × 2 table.
- Select decimal precision and your preferred display style.
- Submit the form to see the completed probability table above the form.
- Review union, conditional, dependence, and association metrics.
- Download the output as CSV or PDF when you need a shareable record.
FAQs
1. What does this probability table calculator do?
It converts four joint outcomes into a complete 2 × 2 probability table. You also get marginal probabilities, conditional probabilities, unions, dependence checks, and exportable summaries.
2. Can I enter counts instead of probabilities?
Yes. In count mode, the calculator divides each cell by the overall total to build the probability table automatically and still reports the observed counts.
3. What happens if my probabilities do not sum to one?
You can allow automatic normalization. The calculator rescales all four values proportionally so the total becomes exactly one before computing the results.
4. How is independence checked?
It compares the observed joint probability P(A ∩ B) with the product P(A) × P(B). A very small gap suggests approximate independence.
5. Why are conditional probabilities sometimes undefined?
A conditional probability needs a nonzero conditioning event. If P(B) or another denominator is zero, the related conditional result cannot be computed safely.
6. When should I use the chi-square statistic?
Use it when your inputs are counts. It compares observed counts with expected counts under independence and helps you judge whether the association looks meaningful.
7. What do phi coefficient and odds ratio show?
They measure association strength. Phi is scaled between negative and positive association, while odds ratio compares how strongly one outcome changes the odds of the other.
8. Is this calculator suitable for teaching and reporting?
Yes. The example table, formulas, readable metrics, and CSV or PDF downloads make it useful for homework, quick analysis, and simple reporting.