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Tuesday, August 16, 2011

Probability


Probability is the branch of mathematics which deals with the study of random phenomenons and probability of occurrence of events.
Some basic probability formulas are:
Notations use in Probability:
p(A) = probability of event A.
p(A \cup B) = probability of event A or B.
p(A \cap B) = probability of event A and B.
Probability Formulas:

1. Probability of an event “A” is:

p(A) = (Number of outcomes favorable to “A”) ÷ (Total numbers of outcomes)

2. For any two events “A” and “B” :

p(A \cup B) = p(A) + p(B) - p(A \cap B)

3. For any three events “A” , “B” and “C”:

p(A \cup B \cup C) = p(A) + p(B) + p(C) - p(A \cap B) - p(B \cap C) - p(C \cap A) + p(A \cap B \cap C)

4. For mutually exclusive events “A” , “B” and “C” ( or if p( A \cap B) = 0and  p(A \cap B \cap C)= 0) :

 p(A \cup B) = p(A) + p(B)

and

 p(A \cup B \cup C) = p(A) + p(B) + p(C)

5. For two independent events “A” and “B”:

 p(A \cup B) = p(A) \times p(B)

and

 p(A \cup B \cup C) = p(A) \times p(B) \times p(c)

6. If A^| is the event complimentary to “A” then:

 p(A^|) = 1 - p(A)

7. If the occurrence of event “A” is dependent on the occurrence of event “B” then:

 p(A \cap B) = p(B) \times  p\left(\frac{A}{B}\right)

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