Conditional Probability and Independence
Events A and B are independent if:
P(A | B) = P(A)
The expression P(A | B) is read as "the probability of A, given that B has occurred)". Alternative phrasings for "given" are "if", "assuming that", and "conditional on"
P(A | B) can often be calculated directly. Alternatively, the formula for conditional probability may be used:
P(A | B) = P(A Ç B) / P(B)
An implication of the formula is that if A and B are independent, then:
P(A Ç B) = P(A) · P(B)
This is sometimes referred to as "the multiplicative rule". Note that it is applicable only when the events A and B are known to be independent. It cannot be used to determine whether A and B are independent.