Probability

Probability

1. What is it?

   • Odds
     • The odds in favor of E are a to b, and the odds agains are b to a.
   • Basic Concepts
     • Outcomes: Possible results of the experiment.
     • Sample space: Set of all possible outcomes.
     • Event: Any such subject of the sample space.
     • Experiment: Any observation measurement of a random phenomenon.
   • Probability Formulas
     • theoretical probability formula
     • Empirical probability Formula

2. Events involving "not" and "or".

   • Probablility of the complement: when E does not occurs- P(not E)=1-P(E)
   • Properties of Probability
     • Probability value: 0<P(E)<1
     • Impossible event: P(E)=0
     • Certain event: P(E)=1
   • Addition rule of probability: P(A or B)=P(A)+P(B)-P(A and B)
     • Mutually exclusive events: no outcomes in comoon

3. Events involving "and"

   • Conditional probability formula
     • P(B/A)=P(A and B)/P(A)
   • Multiplication rule of Probability
     • Independent events: P(A and B)=P(A)xP(B)
     • For any two events: P(A and B)=P(A)-P(B/A)

4. Set operations

   • Intersection
   • Difference
   • Union
   • Complement

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