Bayes' Theorem Calculator
This calculator helps you compute the probability of an event based on prior knowledge of conditions related to the event. It's ideal for statisticians, data scientists, and students studying advanced statistics.
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Data Source and Methodology
All calculations are rigorously based on the formulas and data provided by this authoritative source.
The Formula Explained
\[ P(A|B) = \frac{P(B|A) \cdot P(A)}{P(B)} \]
Glossary of Variables
- P(A): The prior probability of event A.
- P(B|A): The probability of event B given A is true.
- P(B): The total probability of event B.
- P(A|B): The posterior probability of event A given B is true.
How It Works: A Step-by-Step Example
Suppose you want to calculate the probability of having a disease (A) given a positive test result (B). You know that 1% of the population has the disease (P(A) = 0.01), the test is 99% accurate for those with the disease (P(B|A) = 0.99), and 5% of the tests are positive (P(B) = 0.05). Applying Bayes' theorem, the probability of having the disease after a positive test is calculated as above.
Frequently Asked Questions (FAQ)
What scenarios is Bayes' Theorem useful for?
Bayes' Theorem is useful in medical diagnosis, spam filtering, and any scenario where you want to update the probability of a hypothesis based on new evidence.
How does this calculator ensure accuracy?
The calculator uses precise mathematical formulas and is based on authoritative sources to ensure accuracy.