Download Lesson 5.3 Some Probability Rules – Compound Events Mutually

Lesson 5.3 Some Probability Rules – Compound Events
Mutually Exclusive and Addition Rules Notes
Statistics
Page 1 of 4
Sets and Venn Diagrams
Venn Diagram consists of:
 A rectangle that represents the sample space
 Circles within it representing particular events
 A ' is the complement of A. A ' represents the non-occurrence of A.
 x  A : ‘x is in A’, thus x is an element of set A.
 n  A : the number of elements in A



A or B : the union of set A and set B. Represents all the elements in A or B or both A and B.
A and B : the intersection of set A and set B. Represents all the elements in both A and B.
A and B   : the empty set. There is nothing in common.  represents the empty set. Set A
and set B are mutually exclusive if A and B  
Draw a Venn Diagram to represent the following.
The Event A and B
The Event A or B
Example 1: Indicate how each of the following pairs of events are combined. Use either the and
combination or the or combination.
a. Satisfying the humanities requirement by taking a course in the history of Japan or by
taking a course in classical literature.
b. Buying new tires and aligning the tires.
c. Getting an A not only in psychology, but also in biology.
d. Having at least one of these pets: cat, dog, bird, rabbit.
Lesson 5.3 Some Probability Rules – Compound Events
Mutually Exclusive and Addition Rules Notes
Statistics
Page 2 of 4
Example 2: If the Venn diagram alongside illustrates the number of people in a sporting club who
play tennis (T) and hockey (H), determine the number of people:
a. in the club
b. who play hockey
c. who play both sports
d. who play neither sport
e. who play at least one sport
T
15 27 26
H
7
Example 3: The Venn Diagram to the side represents a
sample space, S, of all the children in a class. Each dot
represents a student. The event, A, shows all those
students with blue eyes. Determine the probability that a
randomly selected child:
a. has blue eyes.
b. does not have blue eyes.
E
Mutually Exclusive Events (or disjoint events)
Events are Mutually Exclusive if they cannot occur together. In particular, events A and B are
mutually exclusive if P  A and B   0 .
 Addition rule for mutually exclusive events A and B: P  A or B   P( A)  P( B)
 General addition rule for any events A and B: P  A or B   P( A)  P( B)  P  A and B 
 Using the Addition Rules:
1. Determine if the events are mutually exclusive.
2. If mutually exclusive, use P  A or B   P( A)  P( B)
3. If not mutually exclusive, use P  A or B   P( A)  P( B)  P  A and B 
Lesson 5.3 Some Probability Rules – Compound Events
Mutually Exclusive and Addition Rules Notes
Statistics
Page 3 of 4
Example 4: The Cost Less Clothing Store carries seconds in slacks. If you buy a pair of slacks in
your regular waist size without trying them on, the probability that the waist will be too tight is 0.30
and the probability that it will be too loose is 0.10.
a. Are the events mutually exclusive?
b. If you choose a pair of slacks at random, what is the probability that the waist will be too
tight or too loose?
c. What is the probability that the pants will fit?
Example 5: Professor Jackson is in charge of a program to prepare students for a high school
equivalency exam. Records show that 80 of the students need work in math, 70% need work in
English and 55% need work in both areas.
a. Are the events mutually exclusive?
b. What is the probability that a student selected at random needs math or needs English
help?
Example 6: Laura is playing Monopoly. On her next move she needs to throw a sum bigger than 8
on the two dice in order to land on her own property and pass Go. What is the probability that
Laura will roll a sum bigger than 8?
Example 7: Translate the following phrases into symbols. Consider the following events for a
person selected at random from the general population:
A = person is taking college classes
B = person is under 30 years old
Phrase:
a. The probability that a person is under 30 years old and is taking college classes is 40%
b. The probability that a person under 30 years old is taking college classes is 45%
c. The probability is 45% that a person is taking college classes if the person is under 30.
d. The probability that a person taking college classes is under 30 is 0.60.
e. The probability that a person is not taking college classes or is under 30 years old is 0.75.
Lesson 5.3 Some Probability Rules – Compound Events
Mutually Exclusive and Addition Rules Notes
Statistics
Surveys
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A simple tally survey is a survey that is formed by questions to which the responses can be
recorded in a table called a contingency table.
Example 7: At Hopewell Electronics, all 140 employees were asked about their political affiliations.
The employees were grouped by type of work, as executives or production workers. The results
are shown below.
Political Affiliation
Employee Type
Democrat (D) Republican (R) Independent (I)
Row Total
Executive (E)
5
34
9
48
Production Worker (PW)
63
21
8
92
Column Total
68
55
17
140 (Grand Total)
a. Compute P(D) and P(E).
b. Compute P(D|E).
c. Are D and E independent?
d. Compute P(D and E).
e. Compute P(D or E).
f. Compute P(I) and P(PW).
g. Compute P(I|PW).
h. Compute P(I and PW).
i. Use the multiplication rule for dependent events to calculate P(I and PW). IS the result the
same a h?
j. Compute P(I or PW). Are the events mutually exclusive?
Assignment: p. 180 # 1, 4, 9, 18, 19, 20, 22