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==In Two Events== | ==In Two Events== | ||
| + | Two events A and B are independent if the following formula holds: | ||
<math>P(A \bigcap B) = P(A) \times P(B) </math> | <math>P(A \bigcap B) = P(A) \times P(B) </math> | ||
Revision as of 11:59, 8 September 2008
Independence
In Two Events
Two events A and B are independent if the following formula holds:
$ P(A \bigcap B) = P(A) \times P(B) $
For example, given a coin, are the two outcomes independent?
$ P( \lbrace C_1=H \rbrace \bigcap \lbrace C_2 =H \rbrace ) = 1/4 $
$ P( C_1=H ) \times P(C_2=H) = 1/2 \times 1/2 = 1/4 $
Since the product of the two probabilities is equal to overall probability, the events are independent.
In Multiple Events
$ \bigcap_{i \in S} A_i = \prod_{i \in S} P(A_i) $
Conditional Probability
A & B are conditionally independent given C if the following formula holds true.
$ P(A \bigcap B|C) = P(A|C) \times P(B|C) $
