Probability

Bayes' Theorem Formula - Probability

Learn the bayes' theorem formula with examples, step-by-step guide, and calculator tools. Calculate posterior probability using prior probability and likelihood

The bayes' theorem formula is a fundamental concept in probability. Calculate posterior probability using prior probability and likelihood. This page provides a comprehensive guide with worked examples and practical applications.

The Formula

\[P(A|B) = \frac{P(B|A) \cdot P(A)}{P(B)}\]

Variables

P(A|B)
Posterior probability
P(B|A)
Likelihood
P(A)
Prior probability
P(B)
Marginal probability

Step-by-Step Guide

  1. 1

    Step 1: Gather your data values

  2. 2

    Step 2: Apply the formula

  3. 3

    Step 3: Perform the calculations

  4. 4

    Step 4: Interpret the result

Examples

Example 1

Example 1: [0.9,0.05,0.1] → P(A|B) = (0.9 × 0.05) / 0.10 = 0.45

Example 2

Example 2: 0.45

Frequently Asked Questions

What is the bayes' theorem formula?

Calculate posterior probability using prior probability and likelihood

How do I calculate bayes' theorem formula?

Use the formula: P(A|B) = \frac{P(B|A) \cdot P(A)}{P(B)}. Follow the steps provided above.

What tools can help with bayes' theorem formula?

We provide online calculators: statistics-calculator

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