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Probability

1. Basic Concepts

   • Outcomes
     • Possible effects obtained from an experiment. 
   • Sample espace
     • Set of all posibke results. 
   • Events
     • Sub-set of the sample space. 
     • NOT
       • P(notE)= 1 - P(E)
     • OR
       • P(A or B)= P(A) + P(B) - P(A and B) 
       • Mutually exclusive
         • P(A or B)= P (A) + P(B) 
     • AND
       • Conditional formula
         • P(B/A)= P (A and B) / P(A) 
       • Multiplication Rule
         • Independent
           • P(A and B)= P (A)* P(B) WITH REPLACEMENT 
         • For any two/ Dependent
           • P (A and B)= P(A) * P(B/A) WITH OUT REPLACEMENT. 
   • Experiments
     • Random phenomena. 

2. Odds

   • If a number A of a rersult are fovarable to event E there is A number of events that are not favorable. 

3. Formulas

   • Theroretical
     • P(E)= # of fav. results / total # of results 
   • Empirical
     • P(E)= # of times that an E occurs/ # of times that E is perfomed 

4. Properties

   • Probabiltity Value
     • P(E) 
   • Impossible event
     • P(0)=0 
   • Certain event
     • P(S)=1

5. Venn Diagrams

   • Intersection
     • AND  ONLY THE MIDDLE PART OF THE CIRCLE. 
   • Union
     • OR  THE TWO CIRCLES. 
   • Complement
     • ¨Everything that are not the circles. 
   • Difference
     • ONLY ONE PART OF THE CIRCLE.