7.1 Probability: part 2

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Relative frequency vs. Probability

There are two approaches to determining the probability associated with any particular event of a random experiment:

1. determining the total number of possible outcomes and calculating the probability of each outcome using the definition of probability
2. performing the experiment and calculating the relative frequency of each outcome

Relative frequency is defined as the number of times an event happens in a statistical experiment divided by the number of trials conducted.

It takes a very large number of trials before the relative frequency of obtaining a head on a toss of a coin approaches theprobability of obtaining a head on a toss of a coin (in fact, if the probability of an event occurring is something other than 1, i.e. it is always true, or 0, i.e. it is never true, then probability is only absolutely accurate when an infinite number of trials is conducted). For example, the data in [link] represent the outcomes of repeating 100 trials of a statistical experiment 100 times, i.e. tossing a coin 100 times.

 H T T H H T H H H H H H H H T H H T T T T T H T T H T H T H H H T T H T T H T T T H H H T T H T T H H T T T T H T T H H T T H T T H T T H T H T T H T T T T H T T H T T H H H T H T T T T H H T T T H T

The following two worked examples show that the relative frequency of an event is not necessarily equal to the probability ofthe same event. Relative frequency should therefore be seen as an approximation to probability.

Determine the relative frequencies associated with each outcome of the statistical experiment detailed in [link] .

1. There are two unique outcomes: H and T.

2.  Outcome Frequency H 44 T 56
3. The statistical experiment of tossing the coin was performed 100 times. Therefore, there were 100 trials, in total.

4. $\begin{array}{ccc}\hfill \mathrm{Probability of H}& =& \frac{\mathrm{frequency of outcome}}{\mathrm{number of trials}}\hfill \\ & =& \frac{44}{100}\hfill \\ & =& 0,44\hfill \\ \\ \hfill \mathrm{Relative Frequency of T}& =& \frac{\mathrm{frequency of outcome}}{\mathrm{number of trials}}\hfill \\ & =& \frac{56}{100}\hfill \\ & =& 0,56\hfill \end{array}$

The relative frequency of the coin landing heads-up is 0,44 and the relative frequency of the coin landing tails-up is 0,56.

Determine the probability associated with an evenly weighted coin landing on either of its faces.

1. There are two unique outcomes: H and T.

2. There are two possible outcomes.

3. $\begin{array}{ccc}\hfill \mathrm{Relative Frequency of H}& =& \frac{\mathrm{number of favourable outcomes}}{\mathrm{total number of outcomes}}\hfill \\ & =& \frac{1}{2}\hfill \\ & =& 0,5\hfill \\ \\ \hfill \mathrm{Relative Frequency of T}& =& \frac{\mathrm{number of favourable outcomes}}{\mathrm{total number of outcomes}}\hfill \\ & =& \frac{1}{2}\hfill \\ & =& 0,5\hfill \end{array}$

The probability of an evenly weighted coin landing on either face is $0,5$ .

Project idea

Perform an experiment to show that as the number of trials increases, the relative frequency approaches the probability of a cointoss. Perform 10, 20, 50, 100, 200 trials of tossing a coin.

Interpretation of probability values - (not in caps, included for completeness)

The probability of an event is generally represented as a real number between 0 and 1, inclusive. An impossible event has aprobability of exactly 0, and a certain event has a probability of 1, but the converses are not always true: probability 0 events are not always impossible,nor probability 1 events certain. There is a rather subtle distinction between "certain" and "probability 1".

where we get a research paper on Nano chemistry....?
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
ya I also want to know the raman spectra
Bhagvanji
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
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