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

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