they all come from the definition of conditional probability:
and the associative law of intersection of sets:
The last law allaws you to write the left or right side of the equality as
Im terrible at proofs....
Use the definition of conditional probabilities to prove that any events A, B, C, D, E and F,
P(A B C D E F) = P(A B C D E F)P(E F)
and P(A B C D E F) = P(A B C D E F)P(C D E F)P(F)
Also, can anyone form a similar identity?