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Multiplication Theorem on Probability

If A and B are the events associated with a random experiment then

provided P(A)≠ 0
and
provided P(B)≠ 0

Extension of Multiplication Theorem

If A, B and C are three events associated with a random experiment, then


If A₁, A₂....A_n are associated with a random experiment, then

Independent Events

Two events are called independent if the occurrence or non-occurence of one does not affect the probability of the occurence of the other.

Two events A and B associated with a random experiment are independent if

provided P(B)≠ 0

andprovided P(A)≠ 0

Also


If A₁, A₂....A_n associated with a random experiment are independent then

Theorem

If A, B are independent events, then so are

or

or

or