Probability

Probability

1. odds

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

2. events

   • not
     • properties
       • propertie value
         • a number from 0 througt one
       • certain event
         • dividing all members of this inequality by n(s)gives .
     • impossible event
       • if e is impossible then n(e) must be zero and e is the empty set so
   • or
     • adition rule of probability
       • if a and b are mutually exclusive then
         • p(A)+p(B)
           • mutually exlclusive are 2 events a and b when they have no outcomes in common.
       • if a and b are only two events then
         • a +b -(a & b)
   • probability of the compliment
     • the probability that an event E will not occur is the equal to one minus the probability that it will occur
   • and
     • conditional rule of probability
       • p(a\b)= (a intercetion b)\p(a)
         • = p (a&b)\p(a)
           • conditional probability of b given a
     • multiplication probability formula
       • for any two events
         • p(a)X (b\a)
       • for independent events
         • p(a&b) =(a) x (b)

3. basic concepts

   • outcomes
     • the possible results of the experiments
   • sample sapce
     • set of all possible outcomes
   • event
     • any such subset of the sample space
   • experiments
     • any observation measurement of a random phenomenom

4. Probabiility formulas

   • empirical
     • number of times event ocured\number of times the experiment was performed
   • theorical
     • number of favorable outcomes \total number of outcomes

5. venn diagrams

   • set operationes
     • union
       • aUb {xix a or x E B]
     • difference
       • a-b={(x,y)lx A and y E B]
     • intersection
       • A n B {xlx A or x E A ]
     • complement
       • A´ = {xlx E u x E A]