If we wish to calculate the joint probability of a number of events
happening, it is possible to break the calculation up into a series of
simpler calculations. Formally,
P(A,B,C,D,E)=P(E|A,B,C,D).P(D|A,B,C).P(C|A,B).P(B|A).P(A).
This result follows naturally from the result that
P(The events A and B both happening) =P(The first event, A, happening). P(The second event, B, happening, given that the first event, A, has just happened).