Case
Introduction to The Probability Theory.
- Course
- Probability Theory.
- Institution
- University Of South Africa (Unisa)
A masterclass on elementary probability from Emmanuel Makotsi, the author of "Elementary Statistics"
[Show more]
Seller
Follow
Content preview
THE MATHEMATICS OF UNCERTAINITY(PROBABILITY)
“WRITTEN BY EMMANUEL MAKOTSI”
The purpose of these study notes is to introduce you to some
elementary aspects of the probability theory.
Introduction.
The world we live in is defined by uncertainties.
No one knows when they are going to die.
No one knows with certainty which horse is going to win a race.
More so, it is not even possible for one to predict with certainty
how they will be feeling tomorrow.
The idea of probability according to Mathematical history arises
in 1654, when Chevalier de Mere, a wealthy Frenchman with a
habit of gambling proposed to Blaise Pascal, a Mathematician
of the 17th century how the prize money of a simple game of
chance would be divided between two players if the game is
terminated before either one player wins.
Pascal then communicated the question with another famous
mathematician of that time, Pier de Fermat.
Both Pascal and Fermat arrived at the same answer to the
problem however their methods of solution were different.
The answers were based on the probability or likelihood each
player had on winning the game.
From this idea, a new field of Mathematics emerged.
By 1713, Jacob Bernoulli anticipated by more than two
centuries, the profound practical influence of the subject by
suggesting that probability might be applied the question of
Government, Law, Economics, and morality.
Essential Definitions
Definition 1
, Probability can be divided as the number of times an event A,
of interest occurs over the total number of times of experiment
was conducted.
Mathematically, this is represented as follows: -
P[A] = number of times A occurs
Total number of times experiment was done
Definitions 2.
A statistical experiment is a random experiment whose
outcome are uncertain.
An example of an experiment is tossing a coin or rolling a die.
Basic properties of probability
1. If an event A cannot occur, then its probability of
occurrence is zero. Mathematically written as: -
P [A] = 0
2. If the event A is certain to happen, then probability of A
occurring is one, given as: -
P [A] = 1
3. A probability value will always lie in the interval zero to one
indicated by the expression: -
0 ≤ P [A] ≤ 1
The higher the probability, i.e. the closer to one the
probability, the more likely the event is to happen.
The lower the probability, thus the less likely the event to
happen.
4. The probability of A not occurring is given by 1minus the
probability of A occurring, Mathematically
P [A] =1 - P [A]
There are a lot if approaches to probability which include: -
the experimental approach
theoretical approach
Experimental approach
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through EFT, credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying this summary from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller MAKOTSI. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy this summary for R150,00. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
53022 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy summaries for 14 years now