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International Baccalaureate Mathematics

Statistics and Probability

Syllabus Content

Use of Bayes’ theorem for a maximum of three events.

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Formula Booklet: 4.13

Bayes’ theorem

$$ P(B|A) = \frac{P(B)P(A|B)}{P(B)P(A|B)+P(B')P(A|B')} $$ $$ P(B_i|A) = \frac{P(B_i)P(A|B_i)}{P(B_1)P(A|B_1)+P(B_2)P(A|B_2)+P(B_3)P(A|B_3)} $$

Bayes' theorem provides a way to determine the probability of an event occurring based on prior knowledge of conditions that might be related to the event. When considering three events, Bayes' theorem can be applied iteratively to update our beliefs about the probabilities of each event as new evidence is presented.

The general formula for Bayes' theorem is:

$$ P(A|B) = \frac{P(B|A) \times P(A)}{P(B)} $$


\( P(A|B) \) is the probability of event A given that event B has occurred.

\( P(B|A) \) is the likelihood of event B occurring given that event A has occurred.

\( P(A) \) is the probability of event A.

\( P(B) \) is the probability of event B.

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