Probability Module 1

Probability Module 1

1. basic concepts

   • outcomes
     • Possible results of an experiment
   • sample space
     • All possible outcomes
   • event
     • subset of sample space
   • experiments
     • Any observation,measurement of a random phenomenon

2. Probability Formulas

   • theoretican
     • P(E)= number of favorable outcomes over total outcomes
   • experimental
     • P(E)= number of times event "E" ocurred over number of times the experiment was performed

3. odds

   • compares favorable outcomes to unfavorable outcomes

4. events using

   • and
     • multiplication rule of probability
       • for any two events
         • P(A and B)=P(A)xP(B/A)
       • for independent events
         • P(A and B)=P(A)xP(B)
     • conditional Probability formula
       • P(B/A=P(A intersection B)/P(A)
         • =
           • P(A and B)/P(A)
             • conditional probability of B given A
   • or
     • addition rule of probability
       • if A and B are only two events
         • P(A or B)=P(A)+P(B)-P(A and B)
       • if A and B mutually exclusive
         • P(A and B)=P(A)=P(B)
         • Mutually exclusive is when two events (A and B) have no outcomes in common
   • Probability of complement is that event E will not occur is equal to 1 minus the probabilty that it will occur
   • not
     • Properties
       • probability value
         • A number from 0 to 1
       • certain event
         • dividing all members of this inequality by n(s) gives. 0<n(E)<n(s)
       • impossible event
         • if E is impossibe then n(s) must be 0 (e) is the empty set so P(E)=0

5. venn diagrams

   • set oerations
     • union
       • AUB={xlx EA or x EB}
     • difference
       • A-B={(x,y)lx AN and y EB}
     • intersection
       • A intersection B {xlx EA or x EB}
     • complement
       • A'={xlx Eu and x EA}