Statistics
Class 12

Bayes Theorem

P(AB)=P(BA)P(A)P(B)P(A|B) = \frac{P(B|A) \cdot P(A)}{P(B)}
0.10.20.30.400.20.40.60.81
P(A|B) = P(B|A) × P(A) / P(B)

Adjust Variables

P(B|A)
pBA =
0.11
P(A)
pA =
0.010.5
P(B)
pB =
0.11

Updates probability based on new evidence. The foundation of Bayesian statistics and modern AI.

Real-World Applications

Medical testing — Updating disease probability after test result.

Email spam detection — Naive Bayes classifier.

Machine learning — Bayesian neural networks.

Weather forecasting — Updating predictions with new data.

Fraud detection — Probability of fraud given transaction pattern.

Legal reasoning — Updating guilt probability with new evidence.

A/B testing — Bayesian optimization of experiments.

Search engines — Relevance ranking.

Autonomous vehicles — Sensor fusion for object detection.

Drug trials — Adaptive clinical trial design.

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