Calculate conditional probability using prior odds and evidence strength. Compare test scenarios and posterior confidence. Save results, tables, and charts for faster statistical review.
This quick Bayes theorem calculator helps estimate posterior probability after new evidence appears. It is useful in statistics, diagnostics, fraud detection, screening, and decision analysis. You can enter a prior probability, test sensitivity, and test specificity to see how evidence changes belief.
The tool also estimates likelihood ratios, evidence probabilities, and expected counts for a chosen sample size. That makes it easier to connect probability theory with practical interpretation. The graph compares prior probability with posterior outcomes after positive and negative evidence.
Export options let you save results as CSV or PDF for reports, assignments, or internal reviews. The example table below shows a realistic use case, while the formula and usage sections explain each step. This layout is designed to keep the workflow simple, direct, and fast.
| Metric | Example Value |
|---|---|
| Prior Probability P(A) | 10% |
| Sensitivity P(B|A) | 92% |
| Specificity P(not B|not A) | 88% |
| False Positive Rate | 12% |
| Posterior P(A|B) | 46.0050% |
| Posterior P(A|not B) | 1.0000% |
| Likelihood Ratio Positive | 7.6667 |
| Likelihood Ratio Negative | 0.0909 |
Posterior after positive evidence:
P(A|B) = [P(B|A) × P(A)] / [[P(B|A) × P(A)] + [P(B|not A) × P(not A)]]
Posterior after negative evidence:
P(A|not B) = [P(not B|A) × P(A)] / [[P(not B|A) × P(A)] + [P(not B|not A) × P(not A)]]
Evidence probability for a positive result:
P(B) = [P(B|A) × P(A)] + [P(B|not A) × P(not A)]
Likelihood ratios:
LR+ = Sensitivity / False Positive Rate
LR- = False Negative Rate / Specificity
Bayes theorem updates a prior belief after new evidence appears. It combines prior probability with sensitivity and false-positive information to estimate the posterior probability.
Use it for medical screening, fraud checks, quality control, spam filtering, and any problem where evidence changes the chance of an underlying event.
A high sensitivity increases true positives, while high specificity reduces false positives. Both strongly influence the posterior probability after a positive or negative result.
No. A positive test can still have a modest posterior probability when the prior probability is low or false positives are common.
Likelihood ratios summarize how strongly a test result shifts belief. Higher positive ratios strengthen evidence, while lower negative ratios better rule conditions out.
Sample size does not change the probability formula. It translates percentages into expected counts like true positives, false positives, true negatives, and false negatives.
Enter percentages from 0 to 100. The calculator converts them to probabilities internally before applying the theorem and reporting the results.
Use the negative posterior when you want the chance of the condition after a negative result. It reflects missed detections and remaining uncertainty.
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.