Probability

Probability

1. Basic Concepts

   • Outcomes: Every single possible answer
   • Sample Space: All possible outcomes
   • Event: A piece of the sample space
   • Experiments: Any observations of a random phenomenon

2. Odds

   • Possibility of getting the desired outcome

3. Events involving "not" and "or"

   • Probability of the compliment
     • P(not E)=1-P(E) will not occur
   • Addition rule of probablity
     • If A and B any two events P(AorB)=P(A)+P(B)-P(A and B)
     • If A and B are mutually exclusive P(AorB)=P(A)+(PB)
       • Mutually Exclusive Events
         • Events that are disjoint sets. "No outcomes in common"

4. Events involving "and"

   • Conditional probabilty formula
     • P(AandB) / P(A)
     • Some other event has happened
   • Multiplication rule of probability
     • For independent events
       • [Event A and B] One of them hasn't any effect on the probability of the other one.
         • P(B/A)=P(B)
         • P(A/B)=P(A)
     • For any two events
       • P(AandB)=(PB/A)
       • If A and B are independent
         • P(AandB)=[P(A)] [P(B)]

5. Set Operations

   • Intersection
     • A∩B={xlx E A and E B}
   • Difference
     • A-B={xlx E A and x Ɇ B}
   • Union
     • A∪B={xlx E A and x E B}
   • Complement
     • P(A')={xlx E ʊ and x Ɇ B}