Tables, histograms, bar graphs and pie charts are the most common visual representations of probability distributions.

1. Can you guess the picture?

2. Can you guess the picture?

3. Can you guess the picture?

4. Can you guess the picture?

5. Can you guess the picture?

6. Visualizing
Probabilites

7. Learning
Objectives
define what is contingency table and Venn
diagram;
illustrates problems using contingency table and Venn
diagram; and
solve problems involving conditional probability;
show perseverance and determination in visualizing
probabilities.

8. Contingency Table
Venn Diagram
Lesson Outline

9. Contingency
Table
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.

10. Suppose a study of
speeding violations and
drivers who use cell
phones produced the
following fictional data:
a. Find P (Driver is a cell phone user).
b. Find P (driver had no violation in the
last year).
c. Find P (Driver had no violation in the
last year AND was a cell phone user).
d. Find P (Driver is a cell phone user
OR driver had no violation in the last
year).
e. Find P (Driver is a cell phone user GIVEN driver had a
violation in the last year).
(The sample space is reduced to the number of drivers
who had a violation.)
f. Find P (Driver had no violation last year GIVEN driver
was not a cell phone user).
(The sample space is reduced to the number of drivers
who were not cell phone users.

11. a. (number of cellphone users)/(total
number in study)=305/755 or 61/151
b.(number that had no violation)/(total
number in study)=685/755 or
137/151
c. 280/755 or 56/151
d.(685/755+305/755-
280/755)=710/755 or 142/151
e. 25/70 or 5/14
f. 405/450 or 9/10

12. Venn Diagram
A Venn diagram is a picture that represents
the outcomes of an experiment. It generally
consists of a box that represents the
sample space (S) together with circles or
ovals. The circles or ovals represent
events. It can often help us visualize
relationships between events and
compound events. We can visualize the
entire rectangle as the Sample Space and
areas in the circles as corresponding to
probabilities.

13. In a class of 50 students,
30 take Philosophy, 23
take Sociology, and 12
take both.
What is the probability that a randomly selected student?
a) Takes Sociology
b) Takes both Philosophy and Sociology
c) Does not take Philosophy
d) Takes Sociology but not Philosophy
e) Takes Philosophy given Sociology
f) Takes Philosophy or Sociology
g) Takes neither Philosophy nor Sociology
h) Takes Sociology or Philosophy but not
both.

14. a) 23/50
b) 12/50 or 6/25
c) 20/50 or 2/5
d) 11/50
e) 12/23
f) 41/50
g) 9/50
h) 29/50

15. Activity No. 23 A survey of licensed drivers asked whether they had
received a speeding ticket in the last year and whether
their car is red. The results of the survey are shown in
the contingency table to the right.
Find the probability that a randomly selected survey participant:
a. has a red car.
b. has had a speeding ticket in the last year.
c. has a red car and has not had a speeding ticket in the last year.
d. has a red car or has had a speeding ticket in the last year.
e. has had a speeding ticket in the last year given they have a red car.
f. who has received a speeding ticket in the last year also has a red
car.
I. Solve the probability of the
following using the contingency
table.

16. II. Illustrates the problem using Venn diagram and solve the probability of the
following.
Among the 95 books on a bookshelf, 72 are
fiction, 35 are hardcover, and 28 are both fiction
and hardcover.
a) Create a Venn diagram for the information.
b) What is the probability that a book is fiction and paperback?
c) What is the probability that a book is fiction given it is
hardcover?

17. A recent survey asked SINHS’ians students if they
regularly eat breakfast and if they regularly floss their
teeth. Use the completed Venn Diagram to fill in the
corresponding contingency table.
3 49
12
8
Breakfast
Floss
Breakfast No
Breakfast
Total
Floss
No Floss
Total

18. 100 people were asked if they play basketball or badminton.
• 36 said they play basketball
• 56 said they play badminton
• 20 said they play both.
Illustrates this information on a Venn Diagram and
contingency table.
Find the probability that a randomly selected survey
participant:
a) Play basketball or badminton
b) Play basketball and badminton
c) Play badminton given that they play basketball
d) Neither basketball nor badminton