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The following topics will be covered in this lecture:
Probability is a number that is assigned to each member of a collection of events from a random experiment that satisfies the following properties:
- \( P(S) = 1 \) where \( S \) is the sample space
- \( 0 ≤ P(E) ≤ 1 \) for any event \( E \)
- For two events \( E_1 \) and \( E_2 \) with \( E_1 \cap E_2=\emptyset \) \[ P(E_1\cup E_2)=P(E_1)+P(E_2) \]
Probability of a union \[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \]
Courtesy of Montgomery & Runger, Applied Statistics and Probability for Engineers, 7th edition