# probability formulas

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 $p( A \cap B) = 0$ and $p(A \cap B \cap C)= 0$

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

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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