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Probability

1. Basic Concepts

   • Outcomes
     • Possble results of the experiments
   • Sample Space
     • Set of posible outcomes
   • Event
     • Any such subset of the sample space
   • Experiments
     • Any observation,measurement of the random phemomena

2. Events

   • AND
     • Multiplication Rule of Probability
     • Independent Events
   • OR
     • Addition Rule of Probability
       • If A and b are only 2 events
       • If A and B are mutually excusive
         • Mutually exlusive: if they have no outcomes in common
   • NOT
     • Properties
       • Probability value: a number from 0 to 1
       • Certain event: dividing all members of this inequality by n(s) given
       • If E is impossible, then n(e) is 0

3. Formulas

   • Theorical probability: P(E)= number of favorable outcomes / number of total outcomes
   • Empirical probabiliy: number of times the event e occured / number of times the event was performed

4. Odds

   • Comparison of the favorable events and unfavorable events

5. Venn Diagrams

   • Union: AUB= {x|x E A and E B}
   • Difference: A-B = {(x,y)|x An and y E B}
   • Intersection: AintersectionB= {x|xE A or x E B}
   • Complement: A'= {x|xE U and x E A}