Solve conditional and joint probabilities from known values. Check dependence and apply Bayes theorem confidently. Review formulas, examples, exports, and interpretation in one place.
| Scenario | P(A) | P(B) | P(A ∩ B) | P(A|B) | P(B|A) |
|---|---|---|---|---|---|
| Quality test and product approval | 0.60 | 0.50 | 0.30 | 0.60 | 0.50 |
| Customer visit and purchase | 0.40 | 0.70 | 0.28 | 0.40 | 0.70 |
| Alarm trigger and actual event | 0.20 | 0.35 | 0.14 | 0.40 | 0.70 |
Conditional probability measures the chance of event A when event B already happened. The basic formula is P(A|B) = P(A ∩ B) / P(B). This form works only when P(B) is greater than zero.
Reverse conditional probability uses P(B|A) = P(A ∩ B) / P(A). Joint probability can also be derived from a conditional probability. Use P(A ∩ B) = P(A|B) × P(B) or P(A ∩ B) = P(B|A) × P(A).
Bayes theorem rearranges information. It is written as P(A|B) = [P(B|A) × P(A)] / P(B). This helps when reverse evidence is easier to observe than the direct probability.
For independence, compare P(A ∩ B) with P(A) × P(B). If both values match, the events are independent. If they differ, one event changes the likelihood of the other.
A conditional probability calculator helps you measure how one event changes another event. It is useful in statistics, machine learning, finance, medicine, and risk analysis. You can estimate updated likelihoods after new information appears. This makes decisions more informed and more consistent.
This page supports several common probability tasks. You can calculate P(A|B), P(B|A), and P(A ∩ B). You can also apply Bayes theorem and test event independence. These options make the calculator practical for both study and professional work.
Conditional probability focuses on a reduced sample space. When B is already known, outcomes outside B are no longer relevant. The formula divides the joint probability by the probability of the known event. That is why accurate joint and marginal probabilities matter.
Bayes theorem is powerful when reverse evidence is easier to observe. Many real problems start with P(B|A), not P(A|B). In diagnosis, fraud detection, and classification, Bayes theorem converts observed evidence into an updated belief about the hidden event. This step improves interpretation and prediction quality.
Independence means one event does not affect the other. If P(A ∩ B) equals P(A) × P(B), the events are independent. If the values differ, the events are dependent. This comparison helps you detect relationships inside data or process outcomes.
Always enter probabilities as decimals between 0 and 1. Keep the data logically consistent. A joint probability cannot exceed either marginal probability. Also, the conditioning probability must be greater than zero. These checks prevent impossible results and make the calculator more reliable.
CSV export is useful for reporting or spreadsheet analysis. PDF export is helpful for documentation, assignment submission, and audit trails. With formulas, worked steps, and sample data included, this page supports both quick calculations and clear communication.
Conditional probability is the chance of event A occurring after event B is already known to happen. It narrows the sample space to only outcomes inside event B.
P(A ∩ B) is the joint probability. It shows the chance that both event A and event B occur together in the same trial or observation.
Use Bayes theorem when you know P(B|A), P(A), and P(B), but need P(A|B). It is common in diagnosis, spam filtering, classification, and decision analysis.
No. Valid probabilities stay between 0 and 1. If your result exceeds 1, the inputs are inconsistent or the wrong formula was used.
Compare the joint probability with the product of the marginal probabilities. If P(A ∩ B) equals P(A) × P(B), the events are independent.
Enter decimals only in this calculator. For example, 25% should be entered as 0.25. The result is displayed as both a decimal and a percentage.
Because conditional probability divides by the conditioning event. Division by zero is undefined, so P(B) or P(A) must be greater than zero when used in the denominator.
It is used in medical testing, reliability studies, forecasting, customer behavior analysis, finance, and machine learning models that update predictions with new evidence.
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.