# Probability Theory : The science of measuring chance of an event.

Probability : The science of measuring chance of an event. This article gives us the basic information about the probability theory. We humans knowingly or unknowingly use this in our everyday to day life. This article gives the brief description of what is probabilty, its mathematical description and its basic properties.

The words probably, likely, possibly are most common in our day to day life. We generally say things like, "I shall probaby get first in class", "It is likely to rain today", "It is possible that the shares will come down today". Such statements have an element of chance. They are going to occur in future and the chances of occuring is different for each events. We people always want to know about the events which are going to happen in future and estimate their chances of happing. This science of probability tries to find out the likelihood of occuring of these events. Probability gives us a measure of the chance of occuring of an event.

Defination : If an experiment produces results or "n" outcomes in sample space S which are mutually exclusive and equally likely to happen and "m" of them are in favour of a paricular event A, then the probability of A denoted by P(A) is given by ratio m / n.

Also, P(A) = no. of occurances of in favour of event A / total no. of outcomes in sample space S.

Eg. If a coin is tossed one time then the sample space is {HEAD, TAIL}.

Total no. of outcomes in sample space = 2.

If A is the event of getting HEAD, then no. of occurances of in favour of event A = 1.

Therefore the probability of event A is P(A) = no. of occurances of in favour of event A / total no. of outcomes in sample space S.

P(A) = 1 / 2.

Properties of probability.

a) P(A) >= 0.

b) P(S) = 1.

c) P(A union B) = P(A) + P(B). .... if A and B are mutually exclusive events.

a) The first one says that the probaility of an event is always greater than zero. The probability of any event can never be negative.

b) The second one says that the sum of of probalities of all events in sample space is equal to 1. Using this and first property we can say that P(A) <= 1.

c) The last one says that the probability of two mutully exclusive events is equal to sum of individual probabilities. This can be extended to n number of mutuallty exlusive events such that,

P(A union B union C union ..... N) = P(A) + P(B) + P(C) + .... + P(N).