3.11: Formula Review

3.2 Terminology.

\(A\) and \(B\) are events

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

\[
\begin{array}{l}
0 \leq P(A) \leq 1 \\
P(A \mid B)=\frac{P(A \cap B)}{P(B)}
\end{array} \notag
\]

3.3 Independent and Mutually Exclusive Events

If \(A\) and \(B\) are independent, \(P(A \cap B)=P(A) P(B), P(A \mid B)=P(A)\) and \(P(B \mid A)=P(B)\).

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

3.4 Two Basic Rules of Probability.

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

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