Laws of Probability

== Laws ==
*P[A] \in [0,1] 
* P[A^c] = 1 - P[A] 
* P[A \cap B] = P[A | B] P[B] 
* \frac{P[A \cap B]}{P[B]} = P[A | B] 
* P[A \cup B] = P[A] + P[B] - P[A \cap B]
* Law of total probability: P[A] = \int P[A|X = x] dF_X(x) if continuous, or P[A] = \sum_n P[A \cap B_n] = \sum_n P[A|B_n] P[B_n] if discrete.
need to add measure-theory axiomatic-based proofs.