3/28/2016
What is a Venn Diagram?
9.1 – Venn Diagrams and
Probability
Objective:
TSW create a Venn
Diagram and calculate the
probability of an event.
Example 2: Analyzing a Survey
Example 1:
a)
b)
c)
d)
e)
f)
How many
How many
How many
How many
How many
How many
diagram?
people like country?
people ONLY like country?
people like both rap and rock?
people like both rap and country?
people like rock, rap, and country?
total people are represented in this
g) What is the probability that a person chosen at
random will like rock? P(rock) = ?
h) What is the probability that person chosen at random
will like Rock and Rap?
OR probability:
i) What is the probability that a person chosen at
random will like Rock OR Rap?
P(A) + P(B) – P(A and B)
Example: Analyzing a Survey
Construct a Venn diagram. Let F = football,
B = baseball, and H = hockey.
B
F
20
Suppose that a group of 140 people were questioned
about particular sports that they watch regularly and the
following information was produced.
93 like football
40 like football and baseball
70 like baseball
25 like baseball and hockey
40 like hockey
28 like football and hockey
20 like all three
a) How many people like only football?
b) How many people don’t like any of the sports?
Example: Analyzing a Survey
Construct a Venn diagram. Let F = football,
B = baseball, and H = hockey.
F
8
H
B
20
Start with like all 3
20
Subtract to get
5
H
1
3/28/2016
Example: Analyzing a Survey
Example: Analyzing a Survey
Construct a Venn diagram. Let F = football,
B = baseball, and H = hockey.
F
45
20
8
20
B
25
Construct a Venn diagram. Let F = football,
B = baseball, and H = hockey.
F
45
Subtract to get
5
20
8
7
H
Analyzing a Survey
a) How many people like only football?
b) How many people don’t like any of the sports?
Solution
a) 45 like only football
b) 10 do not like any sports
20
7
H
B
25
Subtract total
shown from 140
to get
5
10
c) What is the probability that a person chosen
at random will like ONLY Hockey?
Ex 2 continued:
d) What is the probability that a person chosen
at random will like Baseball?
F
20
45
8
20
7
H
B
25
e) What is the probability that a person chosen
at random will like Baseball OR Football?
5
f) What is the probability that a person chosen
at random will like Baseball AND Football?
10
g)What is the probability that a person chosen
at random will like all three sports?
Homework!!!!
WORKSHEET
2