Thread: Simple probability proof using conditional probabilities

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?

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