Question

Compare and contrast 'probability' and 'possibility.' Include how you would define the two terms - probability and possibility - in a way that clearly defines each, distinguishes them, and describes the differences that are important in the field of statistics. Consider finding an example of the application of the concepts of probability in your own life that illustrates, at least in part, what you described about probability and possibility, and tell us about it. Are meaningful inferential statistics dependent on both probability and possibility? Why or why not? Any other insights or thoughts about the concepts of probability?

Answer 1

In meaning, both Possibility and Probability mean the same, " the chance of occurrence of a particular event or thing." But technically both the terms have a slightly different meaning.

Possibility of happening of any event can be either ​​​​​​ 0 or 1.

It is like determining the possibility, if Yes, it is possible then it is 1.If No, it is not possible, then it's possibility is 1.

So, possibility can take only two values, 0 or 1.

Whereas when we try to determine how likely a particular event will happen, then it is measured between the real numbers in the interval [0,1].

Hence, possibility is like an assertive question,where we get two values either 1 or 0 depending upon a particular event is possible or not possible respectively.

Consider the following real life example:-

Example:-

Consider an experiment of throwing a die. In this experiment we can understand easily about both Possibility and Probability.

Here,

Possibility can be studied as follows:-

Consider an event of getting a number 4 on a die throw. Here the possibility of event getting a 4 is 1.

Also, consider an event of getting a number 7 on a die throw.

Here the possibility of getting a number 7 is 0.

Now, consider the case of probability

Probability can be studied as follows:-

Consider the event of getting a number 4 on a die throw. Here the probability of event getting a number 4... Means how likely it is to get a number 4 in throwing a die.

Hence, the probability of the event is (1/6) whereas the possibility of the same event is 1.

This is the difference between possibility and probability.

Yes, meaningful inferential statistics are dependent on both...But... They are more dependent on Probability than possibility . Because possibility is not used as much as probability.

The possibility can be used to obtain the Indicator Function. Which can also be called as a probability.

So, basically possibility is a subset or a part of probability.

The term probability has no meaning unless and until it is attached to some event.

In this way, we can study the difference between Possibility and Probability.