Bayes' theorem in words.

Bayes' theorem in words.

• A. The probability of an event equals its prior probability.
• B. The probability of data given the event divided by total data.
• C. The probability of an event given data equals prior times likelihood, normalized.
• D. The probability of the data equals prior times likelihood.

Answer: (C)

Bayes' theorem tells you how to update your beliefs after seeing data. It says your updated probability for a hypothesis given the data is proportional to two things: how plausible the hypothesis was before seeing the data (the prior) and how likely the observed data would be if that hypothesis were true (the likelihood). To turn that proportionality into an actual probability, you divide by the total probability of the observed data under all possible hypotheses (the evidence). In plain terms: the posterior is the prior times the likelihood, normalized by how likely the data is overall. This captures the idea of weighing prior belief by how well the data supports that belief and then ensuring the results form a proper probability distribution.

Bayes' theorem tells you how to update your beliefs after seeing data. It says your updated probability for a hypothesis given the data is proportional to two things: how plausible the hypothesis was before seeing the data (the prior) and how likely the observed data would be if that hypothesis were true (the likelihood). To turn that proportionality into an actual probability, you divide by the total probability of the observed data under all possible hypotheses (the evidence). In plain terms: the posterior is the prior times the likelihood, normalized by how likely the data is overall. This captures the idea of weighing prior belief by how well the data supports that belief and then ensuring the results form a proper probability distribution.