Probability Calculus

Let File:Hepa img850.gif denote arbitrary events with probabilities File:Hepa img851.gif  . Define as the event complementary to A, hence with probability 1-P(A). Let AB be an event for which both A and B are true, and let P(B|A) denote the probability of an event B occurring under the condition that A is given. The Kolmogorov axioms can then be written in the following form:

• a) File:Hepa img852.gif ,
• b) P(E) = 1 (E is the unit, or any event),
• c) File:Hepa img853.gif (for A,B mutually exclusive),
• d) P(AB) = P(A)P(B|A).

Rules:

• i) File:Hepa img854.gif
• ii) File:Hepa img855.gif
• iii) File:Hepa img856.gif for File:Hepa img850.gif mutually exclusive ( sum rule),
• iv) File:Hepa img857.gif for n mutually exclusive events File:Hepa img858.gif (rule of total probability),
• v) P(AB) = P(A) P(B) for independent events A and B.

 also Boolean Algebra.

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