§4.4–Contingency Tables
Joint and Marginal Probabilities
Tom Lewis
Fall Term 2009
Tom Lewis ()
§4.4–Contingency Tables Joint and Marginal Probabilities
Fall Term 2009
1/4
Outline
1
Contingency tables
Tom Lewis ()
§4.4–Contingency Tables Joint and Marginal Probabilities
Fall Term 2009
2/4
Contingency tables
SunRise Run Contingency Table
The following table represents the results of the 2009 SunRise run. The
rows represent the age groups (rounded to the nearest 10) and the
columns represent the finish times (rounded to the nearest 5).
10
20
30
40
50
60
70
80
90
25 30 35 40 45 50 55 60 65 70 75 80 90 95
0 0 2 1 2 5 2 1 0 0 0 0 0 0
1 8 15 11 7 6 5 2 3 0 1 0 0 0
1 9 32 38 31 24 7 6 6 1 3 3 0 0
1 5 29 38 41 33 17 15 4 4 2 2 0 1
0 11 21 29 22 16 15 6 4 5 2 1 0 1
0 0 6 8 12 7 5 2 3 0 1 0 2 1
0 0 2 3 1 1 0 1 0 0 0 0 0 1
0 0 0 0 0 0 0 0 0 0 1 0 0 0
0 0 0 0 0 0 0 0 0 1 0 0 0 0
Tom Lewis ()
§4.4–Contingency Tables Joint and Marginal Probabilities
Fall Term 2009
3/4
Contingency tables
Problem
Let A10 , A20 , . . . , A90 denote the age category events, and let
T25 , T30 , . . . , T95 denote the time category events.
A probability experiment consists of selecting a runner at random from all
of the participants. Use the table to answer the following questions:
Tom Lewis ()
§4.4–Contingency Tables Joint and Marginal Probabilities
Fall Term 2009
4/4
Contingency tables
Problem
Let A10 , A20 , . . . , A90 denote the age category events, and let
T25 , T30 , . . . , T95 denote the time category events.
A probability experiment consists of selecting a runner at random from all
of the participants. Use the table to answer the following questions:
1
What is the total number of participants?
Tom Lewis ()
§4.4–Contingency Tables Joint and Marginal Probabilities
Fall Term 2009
4/4
Contingency tables
Problem
Let A10 , A20 , . . . , A90 denote the age category events, and let
T25 , T30 , . . . , T95 denote the time category events.
A probability experiment consists of selecting a runner at random from all
of the participants. Use the table to answer the following questions:
1
What is the total number of participants?
2
What is P(A40 ∩ T55 )?
Tom Lewis ()
§4.4–Contingency Tables Joint and Marginal Probabilities
Fall Term 2009
4/4
Contingency tables
Problem
Let A10 , A20 , . . . , A90 denote the age category events, and let
T25 , T30 , . . . , T95 denote the time category events.
A probability experiment consists of selecting a runner at random from all
of the participants. Use the table to answer the following questions:
1
What is the total number of participants?
2
What is P(A40 ∩ T55 )?
3
What is P(A40 )?
Tom Lewis ()
§4.4–Contingency Tables Joint and Marginal Probabilities
Fall Term 2009
4/4
Contingency tables
Problem
Let A10 , A20 , . . . , A90 denote the age category events, and let
T25 , T30 , . . . , T95 denote the time category events.
A probability experiment consists of selecting a runner at random from all
of the participants. Use the table to answer the following questions:
1
What is the total number of participants?
2
What is P(A40 ∩ T55 )?
3
What is P(A40 )?
4
What is the chance that the selected runner is in an age group greater
than or equal to 30 but in a time category less than or equal to 30?
Tom Lewis ()
§4.4–Contingency Tables Joint and Marginal Probabilities
Fall Term 2009
4/4
Contingency tables
Problem
Let A10 , A20 , . . . , A90 denote the age category events, and let
T25 , T30 , . . . , T95 denote the time category events.
A probability experiment consists of selecting a runner at random from all
of the participants. Use the table to answer the following questions:
1
What is the total number of participants?
2
What is P(A40 ∩ T55 )?
3
What is P(A40 )?
4
What is the chance that the selected runner is in an age group greater
than or equal to 30 but in a time category less than or equal to 30?
5
What is the most probable age group?
Tom Lewis ()
§4.4–Contingency Tables Joint and Marginal Probabilities
Fall Term 2009
4/4
Contingency tables
Problem
Let A10 , A20 , . . . , A90 denote the age category events, and let
T25 , T30 , . . . , T95 denote the time category events.
A probability experiment consists of selecting a runner at random from all
of the participants. Use the table to answer the following questions:
1
What is the total number of participants?
2
What is P(A40 ∩ T55 )?
3
What is P(A40 )?
4
What is the chance that the selected runner is in an age group greater
than or equal to 30 but in a time category less than or equal to 30?
5
What is the most probable age group?
6
What is the most probable time group?
Tom Lewis ()
§4.4–Contingency Tables Joint and Marginal Probabilities
Fall Term 2009
4/4
Contingency tables
Problem
Let A10 , A20 , . . . , A90 denote the age category events, and let
T25 , T30 , . . . , T95 denote the time category events.
A probability experiment consists of selecting a runner at random from all
of the participants. Use the table to answer the following questions:
1
What is the total number of participants?
2
What is P(A40 ∩ T55 )?
3
What is P(A40 )?
4
What is the chance that the selected runner is in an age group greater
than or equal to 30 but in a time category less than or equal to 30?
5
What is the most probable age group?
6
What is the most probable time group?
7
Do runners slow down with age? Does the data seem to support this
claim?
Tom Lewis ()
§4.4–Contingency Tables Joint and Marginal Probabilities
Fall Term 2009
4/4