Probability

Probability

1. Basic concepts:

   • outcomes:possible results of the experiment sample espace: the set of all possible outcomes event: any such subject of the sample experiments: any observation or measurement of a random phenomenon

2. probability formulas

   • Theoretical probability formula:
     • P(E)=Number of favorable outcomes/ Total number of outcomes
       • n(E) /n(S) .
   • Empirical probability formula:
     • P(E) = Number of times of occurrence of event ‘E’/Total number of observed occurrences

3. Odds

   • compare the number of favorable outcomes to the number of unfavorable outcomes , are commonly quoted

4. Events involving "not" and "or"

   • Properties of probability
     • impossible event:
       • P(E)=0
     • probability value
       • 0≤P(E)≤1
     • certain event
       • P(E)=1
   • Probability of the complement
     • P(not E)=1-P(E)
   • Addition rule of probability
     • A and B, are mutually exclusive (A or B) = P(A) + P(B)
       • Mutually exclusive events
         • P(E)=1-P(E)
     • A and B, are non-mutually exclusive P(A or B) = P(A) + P(B) - P(A and B)

5. Events involving "and"

   • Multiplication Rule of Probability
     • for independent events
       • 2 events A and B called independent events ,the occurrence of one of the has no effect on the probability of the another if: P(B|A)=P(B) OR P(A|B)=P(A)
       • If A and B are independent events then P(A and B) = P(A) * P(B)
     • for any 2 events
       • if A and B are any 2 events then: P(A and B)=P(A)*P(B|A)
   • Conditional Probability Formula
     • The probability of event B occurring that event A has already occurred is read "the probability of B given A" and is written: P(B|A)
       • P(A|B)=P(A ∩ B)/ P(A)
         • = P(A and B)/ P(A)

6. Set Operations

   • intersection
     • A ∩ B= { x | x ∈ A or x∈ B }
   • difference
     • A - B = { x | x∈ A and x∉ B}
   • Union
     • A ∪ B={ x | x ∈ A or x ∈ B }
   • complement
     • A'={ x | x∈∪ A and x∈A}

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