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Conditional Probability

Conditional probability is the probability of some event A , given the occurrence of some other event B . This is denoted P ( A | B ) and is read “the probability of A , given B ”. In other words, we are calculating probabilities conditional on knowing further information partway through the experiment.

     P ( A | B ) = P ( A B ) P ( B )


A math teacher gave her class two tests. 30 % of the class passed both tests and 45 % of the class passed the first test. What percent of those who passed the first test also passed the second test?

P ( Second | First ) = P ( First and Second ) P ( First ) = 0.30 0.45 = 2 3 = 66.7 %

Two-thirds or approximately 66.7 % of the class passed the second test.


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