Analyze dependent and independent events from flexible inputs. See intersections, complements, and verification checks instantly. Build accurate probability insights with clean exports and examples.
| Scenario | P(A) | P(B) | Independent P(A ∩ B) | P(A ∪ B) | P(A | B) |
|---|---|---|---|---|---|
| Machine passes test and ships today | 0.60 | 0.35 | 0.21 | 0.74 | 0.60 |
| Student solves question and checks answer | 0.45 | 0.50 | 0.225 | 0.725 | 0.45 |
| Customer opens email and visits page | 0.25 | 0.30 | 0.075 | 0.475 | 0.25 |
For independent events, one event does not change the other event’s probability.
The verification table compares any observed joint or conditional input with the independent expectation. If the difference stays within the chosen tolerance, the observed values are treated as consistent with independence.
An independent conditional probability calculator helps you study how two events work together. In probability, independence means one event does not affect the chance of the other. This matters in exams, forecasting, quality checks, and many business decisions. Instead of computing each measure by hand, you can enter the known values once and get a complete probability summary.
Many learners confuse independence with mutual exclusivity. They are not the same. Independent events can happen together. Mutually exclusive events cannot happen together. This calculator makes that difference easier to see because it shows the intersection, the union, and the conditional values in one result block. It also shows complement probabilities, so you can inspect the full event structure.
When you know P(A) and P(B), the main independent formula is direct. You multiply them to get P(A ∩ B). From there, you can derive P(A | B), P(B | A), the union, and the chance that neither event occurs. If you provide a sample size, the calculator converts each probability into an expected count. That is useful for experiments, transactions, survey records, and classroom examples.
This page also supports observed joint and observed conditional inputs. Those optional fields help you test whether real data behaves like an independent model. The tolerance setting controls how strict the comparison should be. Small differences may be acceptable because of rounding. Large differences often suggest dependence between the events. That makes this tool helpful for checking homework, validating reports, and reviewing risk assumptions with clearer evidence.
The result appears above the form after submission, so the important values stay visible first. Export buttons make it easy to save the tables as CSV or PDF. The page also includes a formula section, an example table, and step guidance. That combination supports both learning and quick professional use. If you want reliable independent conditional probability results with less manual effort, this calculator gives a clean and focused workflow.
Independence means the occurrence of one event does not change the probability of the other event. In that case, conditional probability matches the original event probability.
No. Mutually exclusive events cannot occur together. Independent events can occur together, and their joint probability equals the product of their individual probabilities.
Because event B does not change the likelihood of event A. Under independence, conditioning on B leaves A unchanged, so P(A | B) equals P(A).
Use it when you already know or measured P(A ∩ B). The calculator compares that value with the independent expectation to test whether independence is plausible.
Tolerance sets the allowed difference between observed values and independent expectations. It helps account for rounding and small reporting gaps during verification.
Yes. Switch the input scale to percent mode. The calculator will convert those values internally and display the results in the same style.
Expected counts translate abstract probabilities into estimated frequencies. This is useful when working with surveys, transactions, tests, or repeated trials.
That usually means the data suggests dependence, not independence. One event may be affecting the chance of the other, or the inputs may contain rounding issues.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.