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This module serves as the complementary teacher's guide for the Probability Topics chapter of the Elementary Statistics textbook/collection.

The best way to introduce the terms is through examples. You can introduce the terms experiment, outcome, sample space, event, probability, equally likely, conditional, mutually exclusive events, and independent events AND you can introduce the addition rule, the multiplication rule with the following example: In a box (you cannot see into it), there are are 4 red cards numbered 1, 2, 3, 4 and 9 green cards numbered 1, 2, 3, 4, 5, 6, 7, 8, 9. You randomly draw one card (experiment). Let R be the event the card is red. Let G be the event the card is green. Let E be the event the card has an even number on it.

    Event card example

  • List all possible outcomes (the sample space). Have students list the sample space in the form {R1, R2, R3, R4, G1, G2, G3, G4, G5, G6, G7, G8, G9}. Each outcome is equally likely. Plane outcome = 1 13 size 12{ { { size 8{1} } over { size 8{"13"} } } } {} .
  • Find P ( R ) size 12{P \( R \) } {} .
  • Find P ( G ) size 12{P \( G \) } {} . G is the complement of R. P ( G ) size 12{P \( G \) } {} + P ( R ) size 12{P \( R \) } {} = _______.
  • P ( size 12{P \( } {} red card given a that the card has an even number on it) = P ( R E ) size 12{P \( R \lline E \) } {} .This is a conditional. Pick the red card out of the even cards. There are 6 even cards.
  • Find P ( R size 12{P \( R} {} AND E ) size 12{E \) } {} . (Multiplication Rule: P ( R and E ) = P ( E R ) ( P ( R ) size 12{E \) =P \( E \lline R \) \( P \( R \) \) } {} )
  • P ( R size 12{P \( R} {} OR E ) size 12{E \) } {} . (Addition Rule: P ( R size 12{P \( R} {} OR E ) = P ( E ) + P ( R ) P ( E size 12{E \) =P \( E \) +P \( R \) - P \( E} {} AND R ) size 12{R \) } {} )
  • Are the events R size 12{R} {} and G size 12{G} {} mutually exclusive? Why or why not?
  • Are the events G size 12{G} {} and E size 12{E} {} independent? Why or why not?

(Optional Topic) A Venn diagram is a tool that helps to simplify probability problems. Introduce a Venn diagram using an example. Example: Suppose 40% of the students at ABC College belong to a club and 50% of the student body work part time. Five percent of the student body works part time and belongs to a club.

Have the students work in groups to draw an appropriate Venn diagram after you have shown them what a Venn diagram basically looks like. The diagram should consist of a rectangle with two overlapping circles. One rectangle represents the students who belong to a club (40%) and the other circle represents those students who work part time (50%). The overlapping part are those students who belong to a club and who work part time (5%).

    Find the following:

  • P(student works part time but does not belong to a club)
  • P(student belongs to a club given that the student works part time)
  • P(student does not belong to a club)
  • P(works part time given that the student belongs to a club)
  • P(student belongs to a club or the student works part time)
  • C

    student belongs to a club
  • Pt

    student works part time

    Find the following:

  • P(a child is 9 - 11 years old)
  • P(a child prefers regular soccer camp)
  • P(a child is 9 - 11 years old and prefers regular soccer camp)
  • P(a child is 9 - 11 years old or prefers regular soccer camp)
  • P(a child is over 14 given that the child prefers micro soccer camp)
  • P(a child prefers micro soccer camp given that the child is over 14)

Tree diagrams (optional topic)

A tree is another probability tool. Many probability problems are simplified by a tree diagram. To exemplify this, suppose you want to draw two cards, one at a time, without replacement from the box of 4 red cards and 9 green cards.

There are (13)(12) = 156 Possible Outcomes. (ex. R1R1, R1R2, R1G3, G3G4, etc.)

    Find the following:

  • P(RR)
  • P(RG or GR)
  • P(at most one G in two draws)
  • P(G on the 2nd draw|R on the 1st draw) . The size of the sample space has been reduced to 12 + 36 = 481 .
  • P(no R on the 1st draw)

Introduce contingency tables as another tool to calculate probabilities. Let's suppose an owner of a soccer camp for children keeps information concerning the type of soccer camp the children prefer and their ages. The data is for 572 children.

Type of Soccer Camp Preference Under 6 6-8 9-11 12-14 Over 14 Row Total
Micro 42 76 46 25 10 199
Regular 8 68 92 105 100 373
Column Total 50 144 138 130 110 572

Assign practice

Assign Practice 1 and Practice 2 in class. Have students work in groups.

Assign lab

The Probability Lab is an excellent way to cement many of the ideas of probability. The lab is a group effort (3 - 4 students per group).

Assign homework

Assign Homework . Suggested problems: 1 - 15 odds, 19, 20, 21, 23, 27, 28 - 30.

Questions & Answers

Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
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
what is the stm
Brian Reply
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?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
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
what is Nano technology ?
Bob Reply
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?
Damian Reply
what king of growth are you checking .?
Renato
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
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
hi
Loga
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
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Source:  OpenStax, Collaborative statistics teacher's guide. OpenStax CNX. Oct 01, 2008 Download for free at http://cnx.org/content/col10547/1.5
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