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We use n ( S ) to refer to the number of elements in a set S , n ( X ) for the number of elements in X , etc.

In a box there are pieces of paper with the numbers from 1 to 9 written on them. A piece of paper is drawn from the box andthe number on it is noted. Let S denote the sample space, let P denote the event 'drawing a prime number', and let E denote the event 'drawing an even number'. Using appropriate notation, in how many ways is it possible to draw: i)any number? ii) a prime number? iii) an even number? iv) a number that is either prime or even? v) a number that is both prime and even?

    • Drawing a prime number: P = { 2 ; 3 ; 5 ; 7 }
    • Drawing an even number: E = { 2 ; 4 ; 6 ; 8 }
  1. The union of P and E is the set of all elements in P or in E (or in both). P E = 2 , 3 , 4 , 5 , 6 , 7 , 8 .

  2. The intersection of P and E is the set of all elements in both P and E . P E = 2 .

  3. n ( S ) = 9 n ( P ) = 4 n ( E ) = 4 n ( P E ) = 7 n ( P E ) = 2
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100 people were surveyed to find out which fast food chain (Nandos, Debonairs or Steers) they preferred. The following results were obtained:

  • 50 liked Nandos
  • 66 liked Debonairs
  • 40 liked Steers
  • 27 liked Nandos and Debonairs but not Steers
  • 13 liked Debonairs and Steers but not Nandos
  • 4 liked all three
  • 94 liked at least one
  1. How many people did not like any of the fast food chains?
  2. How many people liked Nandos and Steers, but not Debonairs?

  1. The number of people who liked Nandos and Debonairs is 27, so this is the intersection of these two events. The number of people who liked Debonairs and Steers is 13, so the intersection of Debonairs and Steers is 13. We are told that 4 people like all three options, and so this means that there are 4 people in the intersection of all three options. So we can work out that the number of people who like just Debonairs is 66 4 27 - 13 = 22 (This is simply the total number who like Debonairs minus the number of people who like Debonairs and Steers, or Debonairs and Nandos or all three). We draw the following diagram to represent the data:
  2. We are told that there were 100 people and that 94 liked at least one. So the number of people that liked none is: 100 94 = 6 . This is the answer to a).
  3. We can redraw the part of the Venn diagram that is of interest:
    Total people who like Nandos: 50
    Of these 27 like both Nandos and Debonairs, and 4 people like all three options. So we find that the total number of people who just like Nandos is: 50 27 4 = 19
    Total people who like Steers: 40
    Of these 13 like both Steers and Debonairs, and 4 like all three options. So we find that the total number of people who like just Steers is: 40 13 4 = 23
    Now use the identity n(N or S) = n(N) + n(S) n(N and S) to find the number of people who like Nandos and Steers, but not Debonairs.
    n(N or S) = n(N) + n(S) n(N and S) 28 = 23 + 19 n(N and S) n(N and S) = 14
    The Venn diagram with that represents all this information is given:
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Activity: venn diagrams

Which cellphone networks have you used or are you signed up for (e.g. Vodacom, Mtn or CellC)? Collect this information from your classmates as well. Then use the information to draw a Venn diagram (if you have more than three networks, then choose only the three most popular or draw Venn diagrams for all the combinations). Try to see if you can work out the number of people who use just one network, or the number of people who use all the networks.

Questions & Answers

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
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
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
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
what is biological synthesis of nanoparticles
Sanket Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Siyavula textbooks: grade 10 maths [caps]. OpenStax CNX. Aug 03, 2011 Download for free at http://cnx.org/content/col11306/1.4
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