Properties

Added by Marlynne Ingram, last edited by Marlynne Ingram on Dec 22, 2008 (view change)

Suppose X is a random variable with sample space denoted by S. Let A and B be subsets of S. We call A and B events. Let A^c be the complement of A (the event that A doesn't happen).

Probability rules

0 = P(A) = 1
P(S) = 1
$P(A \cup B) = P(A) + P(B) - P(A \cap B)$
$P(A \cap B) = P(B \vert A) P(A) = P(A \vert B) P(B)$
$P(A) = P(A \cap B) + P(A \cap B^c)$

Independence

If P(A) = P(A|B), then events A and B are independent.
If A and B are independent, then $P(A \cap B) = P(A) P(B)$
If A and B are independent, then $P(A \cup B) = P(A) + P(B) - P(A) P(B)$ .