Probability

Probability

1. Venn Diagrams

   • Set Operations
     • Difference
       • A-B={(x,y)Ix An and y E B}
     • Intersection
       • AintersectionB {xIx E A or x E B}
     • Complement
       • A´={xIx E U and x E A}
     • Union
       • AUB={xIxE A or x E B}

2. Basic Concepts

   • Outcomes
     • The possible result of the experiment
   • Sample Space
     • Set of all possible outcomes
   • Event
     • Any such subset of the sample space
   • Experiments
     • Any observation or measurement of a random phenomenon

3. Events

   • Not
     • Properties
       • Certain Event
         • Dividing all members of this inequality by n(s) gives. 0<n (E)< n(s)
       • Probability Value
         • A number from 0 through 1
       • Impossible Event
         • If E is impossible then n(e) must be 0 (e) is the empty set so P(E)=0
     • Probability of the Complement
       • The probability that an event E will not occur is the equal to one minus the probability that it will occur.
   • Or
     • Addition rule of probability
       • If A and B are mutually exclusive then:
         • P(A and B)= P(A)+P(B)
           • Mutually exclusive events
             • 2 events A and B are mutually exclusive events if they have no outcomes in common
               • P(A) or P(B)=P(A)+P(B)
       • If A and B are only 2 events
         • P(A or B)=P(A)+P(B)-P(A and B
   • And
     • Conditional Probability Formula
       • P(B/A)=P(A intersection B)/P(A)
         • =
           • P(A and B)/P(A)
             • Conditional Probability of B given A
     • Multiplication Rule of Probability
       • For independent events
         • P(A and B)=P(A)xP(B)
       • For any 2 events
         • P(A and B)= P(A)xP(B/A)

4. Odds

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

5. Probablitity Formulas

   • Theorical Probability
     • P(E)= # of favorable outcomes/total number of outcomes
   • Empirical Probability
     • P(E)=# of times event E occurred/# of times the experiment was performed