Calculator Inputs
Choose a mode, enter your values, and submit. The result appears above this form below the header.
Example Data Table
This example uses 1,000 observations, 400 cases in Event A, 300 cases in Event B, and 180 cases in both events.
| Scenario | Value | Interpretation |
|---|---|---|
| Total observations | 1000 | Complete sample size |
| Count of Event A | 400 | P(A) = 0.40 |
| Count of Event B | 300 | P(B) = 0.30 |
| Count of A and B | 180 | P(A∩B) = 0.18 |
| Conditional probability | 0.60 | P(A|B) = 180 ÷ 300 |
| Reverse conditional probability | 0.45 | P(B|A) = 180 ÷ 400 |
Formula Used
Core formulas
Conditional probability: P(A|B) = P(A∩B) / P(B)
Reverse conditional: P(B|A) = P(A∩B) / P(A)
Joint probability: P(A∩B) = P(A|B) × P(B)
Union: P(A∪B) = P(A) + P(B) - P(A∩B)
Bayes mode
Total probability: P(B) = P(B|A)P(A) + P(B|¬A)P(¬A)
Bayes theorem: P(A|B) = P(B|A)P(A) / P(B)
Independence test: Independent events satisfy P(A∩B) = P(A)P(B)
Lift ratio: Lift = P(A∩B) / (P(A)P(B))
How to Use This Calculator
- Enter custom names for Event A and Event B to match your problem.
- Choose a calculation mode: counts, direct probabilities, or Bayes theorem mode.
- Fill in the required inputs carefully. Counts should be consistent with total cases.
- Click Calculate to display the result above the form below the header.
- Review the metric cards, detailed table, worked steps, and graphs.
- Use the export buttons to save the results as CSV or PDF.
FAQs
1) What does conditional probability mean?
Conditional probability measures the chance of one event happening after you already know another event occurred. It updates the probability using new information.
2) What is the difference between joint and conditional probability?
Joint probability measures both events happening together. Conditional probability measures one event under the condition that the other event has already happened.
3) When is P(A|B) undefined?
It becomes undefined when P(B) equals zero. That means the conditioning event never occurs, so division by zero would be required.
4) Can I use decimals instead of counts?
Yes. Use direct probability mode when you already know P(A), P(B), and P(A∩B). Enter values as decimals between 0 and 1.
5) What does the lift ratio tell me?
Lift compares observed overlap with the overlap expected under independence. Above 1 suggests positive association, below 1 suggests negative association.
6) Can this calculator help test independence?
Yes. Compare P(A∩B) with P(A)P(B). If they are equal or very close, the events are approximately independent.
7) Why does Bayes mode need P(B|not A)?
Bayes mode needs the background rate of Event B among non-A cases. That value helps compute total P(B) before finding P(A|B).
8) What are estimated counts in probability modes?
Estimated counts convert probabilities into approximate frequencies using a chosen reference size. They help you visualize distributions more intuitively.