Probability

Probability

1. Probability (topic)

   • Basic concepts:
     • Outcomes: Possible results of the experiments.
     • Sample space: The set of all possible outcomes.
     • Event: Any such set of the sample space.
     • Experiments: Any observation of measurement of a random phenomenon.
   • Probability formulas:
     • Theoretical probability formula:
     • Empirical probability formula:
   • Odds:
     • Probabilities in favor or against expected outcome. Ex: 1 to 2.

2. Events involving...

   • Not/or:
     • Properties of probability:
       • Certain event: P(S)=1
       • Impossible event: P(Ø)=0
       • Probability value: 0≤P(E)≤1
     • Probability of the complement: P(not E)=1-P(E)
     • Addition rule of probability: If A and B are any two events, then: P(A or B)=P(A)+P(B)-P(A and B).
       • Mutually exclusive events: Two events A and B are mutually exclusive events if they have no outcomes in common. (Mutually exclusive events can't occur simultaneously.) If A and B are mutually exclusive, then: P(A or B)=P(A)+P(B)
   • And:
     • Multiplication rule of probability
       • For any two events: P(A and B)=P(A)*P(B|A)
       • For independent events: P(B|A)=P(B), or equivalently, P(A|B)=P(A)
     • Conditional probability formula: The probability of B, computed on the assumption that event A has happened.

3. Venn diagrams: (Set operations)

   • Intersection: A∩B={x∣x∈A∧x∈B}
   • Union: A∪B={x∣x∈A∨x∈B}
   • Complement: A'={x|x ∈U and ∉A}
   • Difference: A−B={x∣x∈A and x∉B}

4. Luis David Alcalá Díaz A01400383

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