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
$\text{P(person is a car phone user) =}$
$\frac{\text{number of car phone users}}{\text{total number in study}}=\frac{305}{755}$
$\text{P(person had no violation in the last year) =}$
$\frac{\text{number that had no violation}}{\text{total number in study}}=\frac{685}{755}$
$\text{P(person had no violation in the last year AND was a car phone user) =}$
$\frac{280}{755}$
$\text{P(person is a car phone user OR person had no violation in the last year) =}$
$\text{P(F AND C)}\ne \mathrm{P(F)}\cdot \mathrm{P(C)}$ , 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
$\text{M}$ = being male and let
$\text{L}$ = prefers hiking near lakes and streams.
What word tells you this is a conditional?
Fill in the blanks and calculate the probability:
$\text{P(\_\_\_|\_\_\_)}=\mathrm{\_\_\_}$ .
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.
$\text{P(M|L)}=\frac{25}{41}$
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.
$\text{P(F)}=$
$\text{P(P)}=$
$\text{P(F AND P)}=$
Therefore,
$\text{P(F OR P)}=$
$\text{P(F)}=\frac{45}{100}$
$\text{P(P)}=\frac{25}{100}$
$\text{P(F AND P)}=\frac{11}{100}$
$\text{P(F OR P)}=\frac{45}{100}+\frac{25}{100}-\frac{11}{100}=\frac{59}{100}$
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
$\frac{1}{5}\text{}$ and the probability he is not caught is
$\frac{4}{5}\text{}$ . If he goes out the second door, the probability he gets caught by Alissa is
$\frac{1}{4}$ and the probability he is not caught is
$\frac{3}{4}$ . The probability that Alissa catches Muddy coming out of the third door is
$\frac{1}{2}$ and the probability she does not catch Muddy is
$\frac{1}{2}$ . It is equally likely that Muddy will choose any of the three doors so the probability of choosing each door is
$\frac{1}{3}$ .
Door choice
Caught or Not
Door One
Door Two
Door Three
Total
Caught
$\frac{1}{15}\text{}$
$\frac{1}{12}\text{}$
$\frac{1}{6}\text{}$
____
Not Caught
$\frac{4}{15}$
$\frac{3}{12}$
$\frac{1}{6}$
____
Total
____
____
____
1
The first entry
$\frac{1}{15}=\left(\frac{1}{5}\right)\left(\frac{1}{3}\right)$ is
$\text{P(Door One AND Caught)}$ .
The entry
$\frac{4}{15}=\left(\frac{4}{5}\right)\left(\frac{1}{3}\right)$ is
$\text{P(Door One AND Not Caught)}$ .
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
$\frac{1}{15}\text{}$
$\frac{1}{12}\text{}$
$\frac{1}{6}\text{}$
$\frac{19}{60}$
Not Caught
$\frac{4}{15}$
$\frac{3}{12}$
$\frac{1}{6}$
$\frac{41}{60}$
Total
$\frac{5}{15}$
$\frac{4}{12}$
$\frac{2}{6}$
1
What is the probability that Alissa does not catch Muddy?
$\frac{41}{60}$
What is the probability that Muddy chooses Door One
OR Door Two given that Muddy is caught by Alissa?
$\frac{9}{19}$
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?
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
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?
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