3.7: Chapter 3 Formula Review

3.1 Terminology

A and B are events

\(P(S) = 1\) where \(S\) is the sample space

\(0 ≤ P(A) ≤ 1\)

\(P(A | B)=\frac{P(A \cap B)}{P(B)}\)

3.2 Independent and Mutually Exclusive Events

\(\text {If } A \text { and } B \text { are independent, } P(A \cap B)=P(A) P(B), P(A | B)=P(A) \text { and } P(B | A)=P(B)\)

\(\text {If } A \text { and } B \text { are mutually exclusive, } P(A \cup B)=P(A)+P(B) \text { and } P(A \cap B)=0\)

3.3 Two Basic Rules of Probability

The multiplication rule: \(P(A \cap B) = P(A|B)P(B)\)

The addition rule: \(P(A \cup B) = P(A) + P(B) - P(A \cap B)\)