We use
$n\left(S\right)$ to refer to the number of elements in a set
$S$ ,
$n\left(X\right)$ 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:
$E=\{2;4;6;8\}$
The
union of
$P$ and
$E$ is the set of all elements in
$P$ or in
$E$ (or in both).
$P\cup E=2,3,4,5,6,7,8$ .
The
intersection of
$P$ and
$E$ is the set of all elements in both
$P$ and
$E$ .
$P\cap E=2$ .
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
How many people did not like any of the fast food chains?
How many people liked Nandos and Steers, but not Debonairs?
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
$66\u20134\u201327-13=22$ (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:
We are told that there were 100 people and that 94 liked at least one. So the number of people that liked none is:
$100\u201394=6$ . This is the answer to a).
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:
$50\u201327\u20134=19$ 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:
$40\u201313\u20134=23$ Now use the identity
$\mathrm{n(N\; or\; S)}=\mathrm{n(N)}+\mathrm{n(S)}\u2013\mathrm{n(N\; and\; S)}$ to find the number of people who like Nandos and Steers, but not Debonairs.
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
where we get a research paper on Nano chemistry....?
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
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?