Probability

Probability

1. Basic Concepts

   • Outcomes "Possible Results"
   • Sample space "All the possible answers"
   • Event "A piece of the sample space"
   • Experiments "Any observation"

2. Odds

   • Favor "1 to 5"
   • Against "5 to 1"

3. Probability Formulas

   • Theoretical Probability
     • Formula P(e)= #favorable outcomes/total outcomes
   • Empirical Probability
     • Formula P(e)= # of times that e happens/#times that the experiment was performed

4. Events involving "not" and "or"

   • Probability of the Complement
     • P(not e´)= 1-P(e)
   • Addition rule of probability
     • If A and B are any two events
       • P(A or B)= P(A)+P(B)-P(A and B)
     • If A and B are mutually exclusive
       • P(A or B)= P(A) + P(B)
     • Mutually exclusive events
       • "not outcomes in common"
   • Properties of probability
     • Certain Event
       • "1" fact will happen for sure P(s)=1
     • Probability value
       • "0" not going to happen P(o)=0
     • Impossible event
       • "0----->1" 0≤(P(e)≥1

5. Events involving "and"

   • Multiplication Rule
     • for any two items
       • A and B are two events P(A&B)=P(A)*P(B/A)
       • iIf A and B are independent P(A&B)=P(A)*P(B)
     • for independent events
       • Two events A and B one of them has no effect on the probability of the other one.
         • P(B/A)=P(B) or P(A/B)=P(A)
   • Conditional Formula
     • Some other event has happen
       • P(B/A)= P(A∩B)/P(A)

6. Set operations

   • Intersection
     • A∩B= {xIx E A and x E B}
   • Complement
     • (A´)={xIx E A or x E B}
   • Difference
     • A-B={xIx E A and E B}
   • Union
     • AUB={xIx E A or x E B}