Definition

Including the case when events are not independent, joint probabilities can be determined by successive conditioning.

In the case of two events:

$P (A_{1} \cap A_{2}) = P (A_{1}) P (A_{2} ∣ A_{1})$

In the case of three events:

$P (A_{1} \cap A_{2} \cap A_{3}) = P (A_{1}) P (A_{2} ∣ A_{1}) P (A_{3} ∣ A_{2}, A_{1})$

And so on…

Note that you can choose the order of the events, does not have to be exactly as listed above.

Notes