Probability 1.1-1.4

Probability 1.1-1.4

1. Basic concepts

   • Outcomes: possible results of the experiment
   • Sample space: set of all possible outcomes
   • Event: any subset of the sample space
   • Experiments: observation or measurment of a random phenomena
   • Odds: -in favor (1 to 5) -against (5 to 1)
   • Enter text here
   • Probability formulas
     • Theoretical
       • P(E)=n(E)/n(S)= 1/4
     • Empirical
       • P(E)=numer of times event E ocurred/ number of times the experiment was performed
   • Odds: -in favor (1 to 5) -Against (5 to 1)
   • Probability Formulas
     • Theoretical
       • P(E)=n(E)/n(S)=1/4
     • Empirical
       • P(E)= number of times event E occurred/ number of times the experiment was performed

2. Events involving "not" and "or"

   • Properties of probability
     • Impossible event: P(E)=0
     • Certain event: P(E)=1 something always happens
     • Probability value: 0<P(E)<1 percentage of a thing to happen
   • Probability of the complement
     • Probability that on event E will not occur is equal to 1 minus the probability that it will occur P(not E)= 1- P(E)
   • Addition rule of probability
     • A&B --> 2 events then P(A/B)=P(A)+P(B)-P(A and B) A & B --> mutually exclusive then P(A/B)=P(A)+P(B)
       • Mutually exclusive events: no outcomes in common, can't occur simultaneously

3. Events involving "and"

   • Multiplication rule of probability
     • For any 2 events: P(A and B)= P(A). P(B/A)
     • For independent events: if knowledge about the occurrence of one of them has no effect on the probability of the other
       • P(B/A)=P(B) or P(A/B)=P(A) P(A and B)=P(A).P(B)
   • Conditional probability formula
     • P(B/A)=P(AnB)/P(A)=P(A and B)/P(A)
       • Probability of event B computed on the assumption that event A has happened

4. Set Operations

   • Intesection
     • AnB={x|xE A and x E B}
   • Difference
     • A-B={x|xE A and x not E B}
   • Union
     • AuB={x|x E A or x E B}
   • Complement
     • A'={x|x E U and x not E A}

5. Events involving "not" and "or"

   • Properties of probabilities
     • P(E)=1 something always happens
     • Impossible event: P(E)=0
     • Probability value: 0<P(E)<1 percentage of a thing to happen
   • Probability of the complement
     • Probability that on event E will not occur is equal to 1 minus the probability that it will occur P(not E)=1-P(E)
   • Addition rule of probability
     • A,B--> 2 events then P(A/B)=P(A)+P(B)-P(Aand B) A,B--> mutually exclusive then P(A/B)=P(A)+P(B)
       • Mutually exclusive events: no outcomes in common, can´t occur simustaneoulsy

6. Events involving "and"

   • For any 2 events P(A and B)=P(A).P(B/A)
   • For independent events if knowledge about the occurrance of one of them has no effect on the probability of the other
     • P(B/A)=P(B) or P(A/B)=P(A) P(A and B)=P(A).P(B)
   • Conditional probability formula
     • Probability of event B computed on the assumption that event A has happened
       • P(B/A)=P(AnB)/P(A)=P(A and B)/P(A)

7. Set Operations

   • Intersection
     • AnB={x|x E A and x E B}
   • Difference
     • A-B={x|x E A and x not E B}
   • Union
     • AuB={x|x E A or x E B}
   • Complement
     • A'={x|x E U and x not E A}

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