Probability

Probability

1. Basic concepts

   • Outcomes: posible results of the experiment
   • Sample space: set of all possile outcomes
   • Event: subset of the simple space
   • Experiment: any observation, measurement, of a phenomenon

2. Formulas

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

3. Odds

   • # of favorable outcomes vs. # of unfavorable outcomes
     • Odds in favor and odds against

4. Events involving "not" and "or"

   • Addition rule
     • P(E)+(E´)=1
   • Properties
     • Probability value
       • 0≤P(E)≤1
     • Impossible event
       • P(Φ)= 0
     • Certain Event
       • P(S)=1
   • Complement probability
     • P(not E)= 1-P(E)

5. Events involving "and"

   • Conditional Probability Formula
     • P(B/A)=P(A∩B)/P(A)
       • P(B/A)=P(A and B)/P(A)
       • The probability of event E, computed in the assumption that event A has happened.
   • Multiplication Rule of Probability
     • For independent events
       • P(A and B)= P(A) * P(B)
     • For any 2 events
       • P(A and B) = P(A) * P(B|A)

6. Set Operations

   • Intersection
     • A ∩ B={x|x∈ A and x ∈ B}
   • Difference
     • A - B ={x|x∈ A and x ∉ B}
   • Union
     • A ∪ B={x|x∈ A or x ∈ B}
   • Complement
     • A´ ={x|x∈ U and x ∉ A}

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