Bayes Theorem Calculator

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Bayes' Theorem is a fundamental principle in probability theory and statistics that describes how to update the probability of a hypothesis based on new evidence. It provides a way to calculate conditional probabilities.

The theorem is stated mathematically as:

\[P(H | E) = \frac{P(E | H) \cdot P(H)}{P(E)}\]

Where:

1. \( P(H | E) \) is the posterior probability: the probability of hypothesis \( H \) given evidence \( E \).
2. \( P(E | H) \) is the likelihood: the probability of observing evidence \( E \) given that \( H \) is true.
3. \( P(H) \) is the prior probability: the initial probability of hypothesis \( H \) before seeing the evidence.
4. \( P(E) \) is the marginal probability of the evidence \( E \).

In essence, Bayes' Theorem allows us to update our beliefs about the likelihood of a hypothesis as we gather more evidence. It's widely used in fields such as statistics, machine learning, medicine, and decision-making.