Bayes' Theorem describes how to update the probability of a hypothesis when new data is obtained. It reverses conditional probability: instead of asking “what is the probability of the data given the hypothesis?”, we ask “what is the probability of the hypothesis given the observed data?”

P(A∣B) = P(B∣A)*P(A) / P(B)

P(A∣B) = Likelihood × Prior / Marginal likelihood

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P(A∣B) — posterior probability. The probability of hypothesis A after observing data B. This is what we want to find.

P(B∣A) — likelihood. The probability of observing data B if hypothesis A is true.

P(A) — prior probability. The initial probability of the hypothesis before seeing the data.

P(B) — marginal likelihood or evidence.…