<< Chapter < Page Chapter >> Page >
This module introduces the contingency table as a way of determining conditional probabilities.

A contingency table provides a way of portraying data that can facilitate calculating probabilities. The table helps in determining conditional probabilities quite easily. The table displays sample values in relation to two different variables that may be dependent or contingent on one another. Later on, we will use contingency tables again, but in another manner. Contingincy tables provide a way of portraying data that can facilitate calculating probabilities.

Suppose a study of speeding violations and drivers who use car phones produced the following fictional data:

Speeding violation in the last year No speeding violation in the last year Total
Car phone user 25 280 305
Not a car phone user 45 405 450
Total 70 685 755

The total number of people in the sample is 755. The row totals are 305 and 450. The column totals are 70 and 685. Notice that 305 + 450 = 755 and 70 + 685 = 755 .

Calculate the following probabilities using the table

P(person is a car phone user) =

number of car phone users total number in study = 305 755

P(person had no violation in the last year) =

number that had no violation total number in study = 685 755

P(person had no violation in the last year AND was a car phone user) =

280 755

P(person is a car phone user OR person had no violation in the last year) =

( 305 755 + 685 755 ) - 280 755 = 710 755

P(person is a car phone user GIVEN person had a violation in the last year) =

25 70 (The sample space is reduced to the number of persons who had a violation.)

P(person had no violation last year GIVEN person was not a car phone user) =

405 450 (The sample space is reduced to the number of persons who were not car phone users.)

The following table shows a random sample of 100 hikers and the areas of hiking preferred:

Hiking area preference
Sex The Coastline Near Lakes and Streams On Mountain Peaks Total
Female 18 16 ___ 45
Male ___ ___ 14 55
Total ___ 41 ___ ___

Complete the table.

Hiking area preference
Sex The Coastline Near Lakes and Streams On Mountain Peaks Total
Female 18 16 11 45
Male 16 25 14 55
Total 34 41 25 100

Are the events "being female" and "preferring the coastline" independent events?

Let F = being female and let C = preferring the coastline.

  • P(F AND C) =
  • P(F) P(C) =

Are these two numbers the same? If they are, then F and C are independent. If they are not, then F and C are not independent.

  • P(F AND C) = 18 100 = 0.18
  • P(F) P(C) = 45 100 34 100 = 0.45 0.34 = 0.153

P(F AND C) P(F) P(C) , so the events F and C are not independent.

Find the probability that a person is male given that the person prefers hiking near lakes and streams. Let M = being male and let L = prefers hiking near lakes and streams.

  • What word tells you this is a conditional?
  • Fill in the blanks and calculate the probability: P(___|___) = ___ .
  • Is the sample space for this problem all 100 hikers? If not, what is it?
  • The word 'given' tells you that this is a conditional.
  • P(M|L) = 25 41
  • No, the sample space for this problem is 41.

Find the probability that a person is female or prefers hiking on mountain peaks. Let F = being female and let P = prefers mountain peaks.

  • P(F) =
  • P(P) =
  • P(F AND P) =
  • Therefore, P(F OR P) =
  • P(F) = 45 100
  • P(P) = 25 100
  • P(F AND P) = 11 100
  • P(F OR P) = 45 100 + 25 100 - 11 100 = 59 100

Muddy Mouse lives in a cage with 3 doors. If Muddy goes out the first door, the probability that he gets caught by Alissa the cat is 1 5 and the probability he is not caught is 4 5 . If he goes out the second door, the probability he gets caught by Alissa is 1 4 and the probability he is not caught is 3 4 . The probability that Alissa catches Muddy coming out of the third door is 1 2 and the probability she does not catch Muddy is 1 2 . It is equally likely that Muddy will choose any of the three doors so the probability of choosing each door is 1 3 .

Door choice
Caught or Not Door One Door Two Door Three Total
Caught 1 15 1 12 1 6 ____
Not Caught 4 15 3 12 1 6 ____
Total ____ ____ ____ 1
  • The first entry 1 15 = ( 1 5 ) ( 1 3 ) is P(Door One AND Caught) .
  • The entry 4 15 = ( 4 5 ) ( 1 3 ) is P(Door One AND Not Caught) .

Verify the remaining entries.

Complete the probability contingency table. Calculate the entries for the totals. Verify that the lower-right corner entry is 1.

Door choice
Caught or Not Door One Door Two Door Three Total
Caught 1 15 1 12 1 6 19 60
Not Caught 4 15 3 12 1 6 41 60
Total 5 15 4 12 2 6 1

What is the probability that Alissa does not catch Muddy?

41 60

What is the probability that Muddy chooses Door One OR Door Two given that Muddy is caught by Alissa?

9 19

You could also do this problem by using a probability tree. See the Tree Diagrams (Optional) section of this chapter for examples.

Questions & Answers

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
Daniel
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
Maciej
characteristics of micro business
Abigail
Do somebody tell me a best nano engineering book for beginners?
s. Reply
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
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.
Tarell
what is the actual application of fullerenes nowadays?
Damian
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.
Tarell
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.
Virgil
is Bucky paper clear?
CYNTHIA
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.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
AMJAD
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
AMJAD
what is system testing
AMJAD
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
Privacy Information Security Software Version 1.1a
Good
Berger describes sociologists as concerned with
Mueller Reply
Got questions? Join the online conversation and get instant answers!
QuizOver.com Reply
Practice Key Terms 1

Get the best Algebra and trigonometry course in your pocket!





Source:  OpenStax, Collaborative statistics for mt230. OpenStax CNX. Aug 18, 2011 Download for free at http://legacy.cnx.org/content/col11345/1.2
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Collaborative statistics for mt230' conversation and receive update notifications?

Ask