Conditional Probability and Bayes' Theorem
by Froga
An introduction to conditional probability and Bayes' theorem, showing how to update a belief when new evidence arrives. Written for anyone comfortable with basic percentages who wants to see why intuition about tests and probabilities is so often wrong.
Conditional probability asks how likely one event is, given that another event has already happened. P(A|B) means the chance of A, assuming B is true. Bayes' theorem rearranges this: P(A|B) equals P(B|A) times P(A), divided by P(B). P(A) is called the prior — what you believed before any evidence. P(B|A) is the likelihood — how probable the evidence is if A is true. P(B) is the overall chance of the evidence happening at all, counting every way it could occur. The result, P(A|B), is the posterior — the updated belief after seeing the evidence.
In the equation P(A|B) = P(B|A) × P(A) ÷ P(B), what is P(A) called?
multiple choice
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