Comprehensive Calculator Guide
This calculator updates the probability of a hypothesis after evidence. With a 1% prior, 95% detection and a 5% false-positive rate, a positive result means only about a 16% chance of the condition. It explains the result by picturing 1,000 cases.
How it works
P(B) = P(B|A)P(A) + P(B|not A)P(not A); then P(A|B) = P(B|A)P(A) ÷ P(B). Rare hypotheses stay unlikely after one piece of evidence because false alarms among the many outnumber true hits among the few.
How to Use
- Enter the prior P(A).
- Enter P(B|A) and P(B|not A).
- Press “Calculate” to see the posterior.
Formula Used
P(A|B) = P(B|A)P(A) ÷ [P(B|A)P(A) + P(B|not A)(1 − P(A))]
Practical Examples
- Example 1
- 0.01, 0.95, 0.05: posterior ≈ 0.161.
- Example 2
- Spam filter 0.3, 0.8, 0.1: ≈ 0.774.
Important Tips
- Always start from the prior.
- Repeat with the posterior as the new prior.
- Think in 1,000 cases.
Common Mistakes to Avoid
- Ignoring the base rate.
- Confusing P(B|A) with P(A|B).
- Taking P(B|not A) as 1 − P(B|A).
Frequently Asked Questions
- Prior vs posterior?
- Before and after the evidence.
- Where is it used?
- Medicine, spam filters, machine learning.
- Why so low after an accurate test?
- The condition is rare.