Properties

Added by Marlynne Ingram, last edited by Marlynne Ingram on Dec 08, 2007  (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 Ac be the complement of A (the event that A doesn't happen).

Probability rules
  • 0 = P(A) = 1
  • P(S) = 1
  • P(Ac) = 1 - P(A)
  • P(A U B) = P(A) + P(B) - P(A n B)
  • P(A n B) = P(B|A)P(A) = P(A|B)P(B)
  • P(A) = P(A|B) + P(A|Bc)
Independence
  • If P(A) = P(A|B), then events A and B are independent.
  • If A and B are independent, then P(A n B) = P(A)P(B)
  • If A and B are independent, then P(A U B) = P(A) + P(B) - P(A)P(B).

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