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3.11: Formula Review

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

    3.11: Formula Review is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts.