Probability

Probability

1. Basic Concepts

   • Event
     • Subset of the sample space
   • Experiments
     • Any observation or measurement
   • Outcomes
     • Posible results of an experiment
   • Sample Space
     • The set of all possible outcomes

2. Deterministic Phenomenom

   • Can be predicted

3. Random Phenomenom

   • Its value can't be predicted exactly on the basis of obtainable data

4. Probability Formulas

   • Theoretical
     • P(E) = number of favorable outcomes/total number of outcomes = n(E)/n(S)
   • Empirical
     • P(E) = number of times event E ocurred/ number of times the experiment was performed

5. Properties of Prabability

   • Certain Event = P(E) is between 0 and 1
   • Provability Value = P(E) will always be 1
   • Impossible Event = P(E) will always be 0

6. Events Involving "not", "or", "and"

   • "Not"_Probability of the complement: P(not E) = 1 - P(E)
   • "Or"_mutually exclusive events have no outcomes in common
     • P(A or B) = P(A) + P(B) - P(A and B)
     • Mutually Exclusive: P(A or B) = P(A) + P(B)
   • "And"
     • Conditional probability formula:for P(BlA) the formula is P(A n B)/ P(A)
       • Multiplication rule: P(A and B) = P(A) [P(BlA)]
     • Independent events: P(BlA) = P(B) or P(AlB) = P(A)
       • P(A and B) = P(A) P(B)

7. Set of Operations

   • Intersection
     • (A n B)
   • Diference
     • (A - B)
   • Union
     • (A u B)
   • Complement
     • A' or B'