Probability
Probablity is part of our everyday lives. In personal and managerial decisions, we face uncertainity and use probability theory whether or not we admit the use of something so sophisticated. We live in a world in which we are unable to forecast the future with complete certainity. Our need to cope with uncertainity leads us to the study and use of probability theory.
In our day-to-day life involving decision-making problems, we encounter two broad types of problems. These problems can be categorized into two types of models:
Determistic Models cover those situations, where everything realted to the situations is known with certainty to the decision-maker, when decision is to be made. Whereas in Probabilistic Models, the totality of the outcomes is known but it can not be certain, which particular outcome will appear. So, there is always some uncertainty invloved in decision-making. So, probability can also be defined as a measure of uncertainity.
Definition:
Probability is a measure of uncertainity.
In general, probability is the chance something will happen. Probabilities are expressed as fractions \( \frac{2}{3}, \frac{1}{2}, \frac{4}{5} \) or as decimals \( (0.667, 0.500, 0.800) \) between \(zero\) and \(1\). Assigning a probability of \(zero\) means that something can never happen; a probability of \(1\) indicates that something will always happen.
Why we need Probability?
To handle
Experiment
Experiment is the process which produces random outcomes. In an experiment, we provide input and control either the process or variable and then measure the output, which is random.
Consider a person arriving to the reading room in library to read newspaper which are listed on a table. He can choose any newspaper to read such as The Hindu, Business Line, Economic Times, Regional Newspaper, etc., which is a random process. So, the outcomes are uncertain. So, we say the reading process is an experiment.
Sample Space
All possible outcomes of an experiment is called the Sample Space, \(S\)
In our reading newspaper example, the Sample Space is $$ S = (The\: Hindu, Business\:Line, Economic\:Times, Regional\:Newspaper) $$
The Sample Space, \(S\) contains all possible outcomes.
Event
One or more possible outcomes of an experiment is called as an Event, \(E\)
In our reading newspaper example, selecting the newspaper to read is an event which is the outcome of the reading experiment.
Events are classified as:
Events are said to be mutually exclusive if one only one of them can take place at a time. One event preventing the outcome of another event.