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) = $\frac{1}{4}$

## Types of Events

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:
$P(A | B)$ = $\frac { P (A \cap B) } {P ( B )}$

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