Basic Statistics – III – Introduction to Probability

 Probability is a concept which is simple but powerful if applied correctly. A Very Simple example is that when there is coin tossed up,there are two outcomes possible. HEAD and Tail. If the coin has no bias, both the out comes are equally possible. We say that there is a possibility of 50% (0.5) each. Let us extend this to another commonly used game. If we throw a dice, there is a possibility of one out of the six outcomes. The dice will have 6 sides with numbers 1-6 on each side. Here the Probability is 1/6. Meaning each side has a 16.666% (0.01666) chances. In both these cases, assume that each outcome is an event, and  chance of occurrence is called probability.
There are many definitions to Probability.
The simplest is that “The measure of likelihood of occurrences“.The classical definition of probability is stated as below.
If there are “n” Exhaustive, Mutually exclusive and equally likely events, and “m” of them are favorable to an event “E” then the probability of occurrence of event “E”, denoted by Pr[E] is 

Pr[E] = m/n
Here N need to fulfill 3 conditions 1 – Mutually Exclusive (The events are Mutually Exclusive if there is no possibility of them occurring together. Ex : Head and Tail of a same coin.),  2- Collectively Exhaustive (All the possible events are to be taken into account. ex: in the coin it is 2 ) and 3 – Equally Likely ( there shall not be any bias towards any event.)
Statistical (Empirical) definition of Probability:
If an experiment is repeated many times, under identical conditions, then the limit of the ratio of number of times that an event happens(m) to the total number of trials(n), as the umber of trials increases indefinitely, is called as probability of happening of the event. 
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