Probability

Probability

1. Basic Concepts

   • Outcomes
     • possible results of the experiment
   • Sample Space
     • set of all possible outcomes
   • Event
     • subset of the sample space
   • Experiments
     • Observation of a random phenomena
   • Odds
     • Compare number of favorable outcomes to the number of unfavourable outcomes

2. Formulas

   • Theoretical Probability Formula
     • # of favorable outcomes/ total # of outcomes
   • Empirical Probability Formula
     • # of times E happens/ # of times the experiment was performed

3. Events involving "not" & "or"

   • Addition rule of probability
     • If A & B are any 2 events: P(A or B)= P(A) + P(B) - P(A & B)
     • Mutually exclusive events: P(A or B)= P(A) + P(B)
   • Probability of the complement
     • P (not E) = 1- P(E)

4. Properties of Probability

   • Certain even: P(E)= 1
   • Impossible event: P(E)= 0
   • Probability value: 0<P(E)<1

5. Events involving "and"

   • Multiplication rule of probability
     • Independent events
       • of two events one of them has no effect on the other.
         • P(B/A) = P(B)
           • P(A&B)= P(A) · P(B)
     • Any two events
       • P(A&B)= P(A) · P(B/A)
   • Conditional probability formula
     • same other event has happened
       • P(B/A)= P(A&B) / P(A)

6. Set Operations

   • Difference
   • Intersection
   • Union
   • Complement

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