Redefining Probability? Probably.

I am knee-deep in random experiments. Amartya, my teenaged son has his 12^th grade exams coming up, and he seems to have found a simple rebuttal to my ‘Don’t you plan to study’ refrain. It is the simple and effective retort ‘Why don’t you study and teach me? Aren’t you supposed to be a math teacher?’

I have rechristened this simple and ingenious strategy to keep a nagging parent at bay as 'Bayes' Theorem' ... you see, I am studying Probability...

Anyway, my own continued trials and tribulations with my teen terror has inspired me to rethink many of the other terms and examples used in Probability, too. Here are some:

Random Experiment: is defined as an experiment that can be repeated numerous times under the same conditions. Some examples are: the tossing of a coin, the throwing of a die, or calling Amartya every morning to try and get him out of bed.

Now, it should be easy to understand why a random experiment is also known as a ‘trial’...

Subjective probability: describes an individual's personal judgement about how likely a particular event is to occur. It is not based on any precise computation but is often a reasonable assessment by a knowledgeable person.

For example, according to a reasonable assessment made by me, on any given morning, the likelihood of Amartya getting out of bed after being called once  is 0, after being called 25 times is 0.2, and after being called 75 times is 0.5.

Relative Frequency: describes the frequency at which Amartya’s various relatives (his father, sister, grandmother and me) appear in his room to try and get him out of bed.

Impossible Event: is an event that just can NOT happen, whose probability is 0. For example: the event that Amartya wakes up before 11 am on any day when there is no college, including a day immediately preceeding an exam.

Certain Event: An event that is SURE to happen, whose probability is 1. For example: the event that Amartya logs onto FB on any given day of the year, including a day immediately preceeding an exam.

Independent events: are two events that do not affect each other at all - when the probability of an event A occurring is totally independent of another event, B and vice versa.

For example: Let A be the event of Amartya spending more than 5 hours on Facebook on a given day; and B be the event of there being an exam the next day.

Then A and B are independent events - as the probability of A remains 1, it is absolutely unaffected by event B.

And I end by redefining Mutually Exhaustive events...

Mutually Exhaustive Events

The above series of 'Mutually Exhuastive Events' usually ends
 with this - a Mutually Exclusive Event.