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Chapter 12

Conditional probabilities – The Bayes

theorem

Conditional probability is the probability of an event whose calculation is
based on the knowledge that some other event has occurred.

The symbol P(A│B) is read as ‘The probability of A occurring given that B has
already occurred.

P (A and B) = P(A│B) × P (B) P (A and B) = P(B│A) × P (A)

P(A and B) P(B and A)

P(A│B) = ––––––––– P(B│A) = –––––––––

P(B) P(A)

5.1 Contingency tables

Contingency tables are created by taking the given probabilities, multiplying by some
convenient number, typically 100 or 1,000 (to make the numbers easier to work with)
then drawing a table to show the various combinations of factors that may exist.

Illustrations and further practice

Now read illustration ‘Contingency tables’ and try example 5 ‘Conditional
Probabilities’ from Chapter 12.

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