Using Eq. (1), Eq. (3) leads to the following expression for the conditional probability:

It is important to note that the joint probability , the marginal
probability
, and the conditional probability are all legitimate
probabilities,
hence they satisfy the properties given in the box above.
Finally, it is straightforward to generalize these definitions to treat a
three-part experiment that
has a composite event consisting of three events, or in general an **n**-part
experiment with **n** events occurring.

If events and are * independent*, then the probability of one
occurring does not affect the probability of the other occurring, therefore:

Using Eq. (4), Eq. (5) leads immediately to

for independent events and .
This last equation reflects the fact that the
probability of event occurring is independent of whether event has
occurred, * if events and are independent*.