In Example 7, the second event depends on what happened in the first event; this indicates dependent events. Notice that the method for finding probability is the same as for independent events - multiply the probabilities of each event. The difference is in the probabilities themselves.

Because the marbles were drawn without replacement, both the number of blue marbles and the total number of marbles changed. This affects the final probability.

Example 7 illustrates what is known as conditional probability .

For any two dependent events A and B , the probability that event B will happen given that event A has occurred is determined by the following formula.

P ( B | A ) is read, the probability of event B given that event A has already happened .

This formula can be written using set notation.

 

The diagram below illustrates the solution from Example 7 written using the notation P ( B | A ).