Probability

Probability

1. Types of probability

   • Theoretical probability
     • P(E) = number of favorable outcomes/ total number of outcomes = n(E) / n(S)
   • Empirical probability
     • P(E) = number of times event E ocurred / number of times the experiment was performed

2. Venn Diagrams

   • Complement
     • A'= Everything that belongs to A.
   • Intersection
     • Things that A & B got in common.
   • Union
     • A & B juntos. 
   • Difference
     • Everything in A but not what they got in common. 

3. Theory

   • Experiment
     • Any observation, or measurement, of a random phenomenon.
   • Outcome
     • The possible result of an experiment. 
   • Sample space
     • The set of all possible outcomes. 
   • Event
     • Any such subset of the sample space. 
     • Events involving "And"
       • Multiplication rule of probability
         • For any two events
           • P( A and B) = P(A) x P(B/A)
         • For independent events
           • P(B/A) = PxB
           • P(A/B) = PxA
       • Conditional probability formula
         • P (B/A) = P (A and B) / P (A)
           • Some other event has happened.
     • Events involving "Not" and "Or"
       • Addition rule of probability
         • If A and B are only two events. P( A or B) = P(A) + P(B) x P(A and B)  
         • Mutually exclusive events
           • P (A or B) = P(A) + P(B)
         • Non- mutually exclusive events
           • P(A and B) = P(A) x (B)

4. Properties of Probability

   • Inclusive event
     • 0<P(E)<1 The probability of an event is a number from 0 through 1
   • Impossible event
     • P(0)=0
   • Certain event
     • P(S)=1

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