Probality

Probality

1. Odds

   • Compare the number of favorable outcomes to the number of unfavorable outcomes

2. Pobability Formulas

   • Theorical Probability
     • P(E)= Number of favorable outcomes / Total number of outcomes
   • Empirical Probability
     • P(E)= Number of times that event E occurred / Number of times that the experiment has been performed

3. Events

   • And
     • Multiplication rule of probability
       • For any two events
         • P(A and B)= P(A)*P(B/A)
       • For independent events
         • P(A and B)=P(A)*P(B)
     • Conditional probability formula
       • P(B/A)= (AintersectionB)/P(A)
   • Or
     • Addition rule of probability
       • If A and B are mutually exclusive
         • P(A and B)=P(A)+P(B)
           • They have outcomes in common
       • If A and Bare only two events
         • P(A or B)=P(A)+P(B)-P(A and B)
   • Not
     • Properties
       • Probability value
         • 0-1
       • Certain Event
         • Dividing all the members of this inequality by n(s) gives. 0<n(E)<n(s)
       • Impossible Event
         • if E is impossible then n(e) must be 0 (e) is the empty set P(E)=0
     • Probability of the Complement
       • The probability that an even E will not occur if the equal to 1 minus the probability that will occur

4. Venn Diagrams

   • Set Operations
     • Intersection
       • A intersection B {x/x E A or x E B}
     • Complement
       • A'={x/x E U and xE A}
     • Difference
       • A-B{(x,y)/x An and y E B}
     • Union
       • AuB{x/x E A or x E B}

5. Basic Concepts

   • Outcomes
     • Possible results of experiments
   • Sample space
     • Set of all possible outcomes
   • Event
     • Any such subset of the sample space
   • Experiments
     • Measurement of a random phenomena