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
and
.
Calculate the following probabilities using the table
(The sample space is reduced to the number of persons who had a violation.)
(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
= being female and let
= preferring the coastline.
=
=
Are these two numbers the same? If they are, then
and
are independent. If they are not, then
and
are not independent.
, so the events
and
are not independent.
Find the probability that a person is male given that the person prefers hiking near lakes and streams. Let
= being male and let
= prefers hiking near lakes and streams.
What word tells you this is a conditional?
Fill in the blanks and calculate the probability:
.
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.
No, the sample space for this problem is 41.
Find the probability that a person is female or prefers hiking on mountain peaks.
Let
= being female and let
= prefers mountain peaks.
Therefore,
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
and the probability he is not caught is
. If he goes out the second door, the probability he gets caught by Alissa is
and the probability he is not caught is
. The probability that Alissa catches Muddy coming out of the third door is
and the probability she does not catch Muddy is
. It is equally likely that Muddy will choose any of the three doors so the probability of choosing each door is
.
Door choice
Caught or Not
Door One
Door Two
Door Three
Total
Caught
____
Not Caught
____
Total
____
____
____
1
The first entry
is
.
The entry
is
.
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
Not Caught
Total
1
What is the probability that Alissa does not catch Muddy?
What is the probability that Muddy chooses Door One
OR Door Two given that Muddy is caught by Alissa?
You could also do this problem by using a probability tree. See the
Tree Diagrams (Optional) section of this chapter for examples.
the study of living organisms and their interactions with one another and their environment.
Wine
discuss the biological phenomenon and provide pieces of evidence to show that it was responsible for the formation of eukaryotic organelles in an essay form
advantage of electronic microscope is easily and clearly while disadvantage is dangerous because its electronic. advantage of light microscope is savely and naturally by sun while disadvantage is not easily,means its not sharp and not clear
Abdullahi
cell theory state that every organisms composed of one or more cell,cell is the basic unit of life
Abdullahi
is like gone fail us
DENG
cells is the basic structure and functions of all living things
A scanning electron microscope (SEM) is ideal for situations requiring high-resolution imaging of surfaces. It is commonly used in materials science, biology, and geology to examine the topography and composition of samples at a nanoscale level. SEM is particularly useful for studying fine details,
