How to Calculate Bayes Theorem
What is Bayes Theorem?
Applies Bayes theorem updating probability based on new evidence. Foundation of probabilistic reasoning.
Formula
P(A|B) = P(B|A) × P(A) ÷ P(B)
- P
- overall probability of evidence — overall probability of evidence
- A
- likelihood of evidence given A — likelihood of evidence given A
- B
- overall probability of evidence — overall probability of evidence
Step-by-Step Guide
- 1P(A|B) = P(B|A) × P(A) ÷ P(B)
- 2P(A|B) = posterior (updated probability)
- 3P(A) = prior probability
- 4P(B|A) = likelihood of evidence given A
- 5P(B) = overall probability of evidence
Worked Examples
Input
P(A), P(B|A), P(B)
Result
P(A|B) calculated
Common Mistakes to Avoid
- ✕Confusing conditional probabilities
- ✕Not updating priors properly
- ✕Forgetting normalization constant P(B)
Frequently Asked Questions
What's practical example?
Medical test: prior disease probability, test accuracy, posterior if positive test result.
Why is Bayes important?
Foundation of statistical inference, machine learning, and decision-making under uncertainty.
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