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# Section 4.4

### Multiplication Rule

TermDefinition
Notation P(A & B) = P(event A occurs in a 1st trial & event B occurs in a 2nd trial)
Conditional Probability The probability for the 2nd event B should take into account the fact that the 1st event A has already occurred. P(B|A) represents the probability of event B occurring after it is assumed that event A has already occurred (read B|A as "B given A.")
Independent 2 events A & B are independent if the occurrence of one does not affect the probability of the occurrence of the other.
Dependent The occurrence of one of them does affect the probability of the occurrence of the other but this does not necessarily mean that one of the events is a cause of the other.
Formal Multiplication Rule P(A & B) = P(A) X P(B|A) (if A & B are independent events, P(B|A) is really the same as P(B)
Intuitive Multiplication Rule When finding the probability that event A occurs in 1 trial &event B occurs in the next, multiply the probability of event A by the probability of event B, but be sure that the probability of event B takes into account the previous occurrence of event A.
5% Guideline for Cumbersome Calculations If a sample size is no more than 5% of the size of the population, treat the selections as being independent (even if the selections are made without replacement, so they are technically dependent.)
Created by: hfanch24