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This module introduces Venn diagrams as a method for solving some probability problems. This module is included in the Elementary Statistics textbook/collection as an optional lesson.

A Venn diagram is a picture that represents the outcomes of an experiment. It generally consists of a box that represents the sample space S together with circles or ovals. The circles or ovals represent events.

Suppose an experiment has the outcomes 1, 2, 3, ... , 12 where each outcome has an equal chance of occurring. Let event A = {1, 2, 3, 4, 5, 6} and event B = {6, 7, 8, 9} . Then A AND B = {6} and A OR B = {1, 2, 3, 4, 5, 6, 7, 8, 9} . The Venn diagram is as follows:

A Venn diagram. An oval representing set A contains the values 1, 2, 3, 4, 5, and 6. An oval representing set B also contains the 6, along with 7, 8, and 9. The values 10, 11, and 12 are present but not contained in either set.
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Flip 2 fair coins. Let A = tails on the first coin. Let B = tails on the second coin. Then A = { TT , TH } and B = { TT , HT } . Therefore, A AND B = { TT } . A OR B = { TH , TT , HT } .

The sample space when you flip two fair coins is S = { HH , HT , TH , TT } . The outcome HH is in neither A nor B . The Venn diagram is as follows:

Venn diagram with set A containing Tails + Heads and Tails + Tails, and set B containing Tails + Tails and Head + Tails. Head + Heads is contained in neither set, and set A and set B share Tails + Tails.
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Forty percent of the students at a local college belong to a club and 50% work part time. Five percent of the students work part time and belong to a club. Draw a Venn diagram showing the relationships. Let C = student belongs to a club and PT = student works part time.

Venn diagram with one set containing students in clubs and students in clubs and working part-time and another set containing C/PT and students working part-time. Both sets share  C/PT.

If a student is selected at random find

  • The probability that the student belongs to a club. P(C) = 0.40 .
  • The probability that the student works part time. P(PT) = 0.50 .
  • The probability that the student belongs to a club AND works part time. P(C AND PT) = 0.05 .
  • The probability that the student belongs to a club given that the student works part time.
    P(C|PT)  =  P(C AND PT) P(PT)  =  0.05 0.50  =  0.1
  • The probability that the student belongs to a club OR works part time.
    P(C OR PT) = P(C) + P(PT) - P(C AND PT) = 0.40 + 0.50 - 0.05 = 0.85
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Questions & Answers

How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
characteristics of micro business
for teaching engĺish at school how nano technology help us
How can I make nanorobot?
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
how can I make nanorobot?
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
what is the actual application of fullerenes nowadays?
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
1 It is estimated that 30% of all drivers have some kind of medical aid in South Africa. What is the probability that in a sample of 10 drivers: 3.1.1 Exactly 4 will have a medical aid. (8) 3.1.2 At least 2 will have a medical aid. (8) 3.1.3 More than 9 will have a medical aid.
Nerisha Reply
Practice Key Terms 1

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Source:  OpenStax, Collaborative statistics. OpenStax CNX. Jul 03, 2012 Download for free at http://cnx.org/content/col10522/1.40
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