Probability is a measure of occurrence of an event. Probability always lie between the value 0 and 1. If the probability of an event is higher , the more certain will be the event to occur. An event can have one or more outcomes. 

Definition of Probability:

If an experiment produces "N" equally likely outcomes and "n" are favorable outcomes of an event E, then the probability of E is given as
$P(E) = $$\frac{   Number  of  favorable  outcomes}{  Number   of    total   possible   outcomes}$ = $\frac{n}{N}$Example:
Find the probability of tossing two coins simultaneously and obtaining two tail.
Solution:  Possible outcomes = { HH, HT, TH, TT }
              Favorable outcomes = 1

                              P(2 tail) = $\frac{1}{4}$
Complementary Event:
Probability of an event A is P(E). Complement of an event A is the event where the event of A is not occurring.
Probability is given by:
                             $ P(not A) = 1 - P(A)$
                             ${A}' = 1 - P(A)$

Independent Event:
If two events, A and B occur simultaneously, are independent then it is known as intersection probability. The joint probabilty of two events A and B is given as: 
                   $P(A  and  B) = P(A \cap B ) = P(A) P(B)$

Mutually Exclusive:
If either event A or B or both occur at same time, then it is known as Union of the events A and B. The probabilty of mutually exclusive events is given as:
                    $P(A  or  B) = P(A \cup B ) = P(A) + P(B)$
If the events are not mutually exclusive then the probabilty is given as:
                    $P(A \cup B) = P(A) + P(B) - P(A  \cap  B)$

Conditional Probability:
If there is an event A,occurrence of another event B is given,then probabilty is known as conditional probabilty. The probabilty of A,given B is given as:
                    $P(A  |  B)$ = $\frac { P (A  \cap  B) } {P ( B )}$