Probability

Probability

1. Basic Concepts

   • outcomes
     • Posible results
   • Space
     • Set of all possible results
   • Event
     • Sub-set of the sample space
       • not
         • Addition rule
           • P(AUB)=P(A)+P(B)
           • P(AUB)=P(A)+P(B)-P(A∩B)
       • or
         • Mutually Exclusive
           • Can not happen both at the same time.
       • and
         • Multiplication Rule
           • Two events: P(A and B) = P (A) * P(B/A)
           • Independent events: P(A∩B)= P(A)*P(B)
   • Experiments
     • Random phenomena

2. Formulas

   • Theoretical
     • P(E)= #Favorable results / total # of results
   • Empirical
     • P(E)= # of times that an event occurs / # of times the experiment is performed

3. Set operations

   • Intersection
     • A∩B={x|x ∈ A and x ∈ B}
   • Difference
     • A-B={x|x A and x ∉ B)
   • Union
     • AUB={x|x ∈ A or x ∈ B}
   • Complement
     • A'= {x|x ∉ A}

4. Odds

   • Against: B to A
   • In favor: A to B