The Probability

         It is wisely said that ‘the only certain thing in this world is uncertainty’.

If we need to take decisions under uncertain situations, Statistics can prove to be a handy tool.  The decisions taken using Statistics can be justified scientifically. If we do have concrete information regarding the situation, we can base our decision system on this information. But, if the information is not concrete or is probabilistic, then one must use Statistical science. The probabilistic is something which is not certain.  If occurrence of certain event has certain chances, but not 100%, then that event is called probabilistic. If the event is certain to happen, then it’s quite comfortable situation to take decisions. But as we know, life is all about uncertain things. How to deal with this uncertainty then?

If almost all the things are uncertain, then we just can’t ignore this uncertainty. We need to have a science that will deal with uncertain situations in a systematic manner. For instance, consider tossing a fair coin having two faces as Head and Tail. No one will give guarantee that the coin toss will result in Head. There is possibility that coin toss may result in Head, but we can’t guarantee it. One may have variety of concerns regarding this coin tossing experiment such as how many times do one need to toss the coin to get first Head, How many times will one get Head out of, say, 100 tosses. It is obvious that such problems won’t have answers which are always correct. But Statistics can give various answers to such questions with degree of certainty assigned with each answer. Let us consider the problem as how many times do one need to toss the coin to get first Head. It may take only one toss to get first Head, or one may have to conduct more than one tosses to witness first Head. So, the answer can’t be a single number. What Statistics does is assigning a degree of certainty with each possible number. This degree of certainty is called as Probability. So, the Statistical answer to the question- how many times do one need to toss the coin to get first Head- will be {1,2,3,.....} with probability of each number as {P₁.P₂,P₃,...}. Instead of giving answer as one number, we are saying that all numbers are possible as answer, but with different degree of certainty. For example, one may get first Head in 2 tosses with a probability or chance as P₂. Such collection of probabilities is termed as Probability Distribution. Once we get this distribution, we can calculate the ‘average’ number of tosses to get first Head, which will be a single number that will represent the entire distribution.  These probability distributions are the core things of Statistics. One has to first understand basic formulation of distributions to get complete idea about Statistical science.