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Addition Rule for Probability
Complimentary Probability
Addition Rule for Probability
Addition Rule for Probability
Let A and B be events. Then
P(A ∪ B) = P(A) + P(B) − P(A ∩ B).
If A and B are mutually exclusive (A ∩ B = 0/ ), then
P(A ∪ B) = P(A) + P(B)
Dr. Glenn Rice
Section 8.2: Union, Intersection, and Complement of Events
MWSU
Addition Rule for Probability
Complimentary Probability
Examples
An experiment consists of rolling two fair dice. Find the probability of rolling a sum of 7
or a sum of 12.
An experiment consists of rolling two fair dice. Find the probability of rolling a sum that
is greater or equal to 10 or a double.
A single card is drawn from a standard 52-card deck. Calculate the probability that a
king or a heart is drawn. (Exercise 54, Page 396)
Dr. Glenn Rice
Section 8.2: Union, Intersection, and Complement of Events
MWSU
Addition Rule for Probability
Complimentary Probability
Complimentary Probability
Complimentary Probability
Let E be an event. Then
P(E0 ) = 1 − P(E).
Dr. Glenn Rice
Section 8.2: Union, Intersection, and Complement of Events
MWSU
Addition Rule for Probability
Complimentary Probability
Examples
What is the probability of getting at least 1 black card in a 7-card hand dealt from a
standard 52-card deck? (Exercise 58, Page 396)
Dr. Glenn Rice
Section 8.2: Union, Intersection, and Complement of Events
MWSU
Addition Rule for Probability
Complimentary Probability
Examples (continued)
A carton of 24 MP3 players includes 4 that are defective. Four MP3 players are
chosen at random from the carton.
A
B
C
What is the probability that the four defective MP3 players are chosen?
What is the probability that none of the defective MP3 players chosen?
What is the probability that at least one of the four MP3 players chosen is defective?
An assembly plant produces 40 outboard motors, including 7 that are defective. The
quality control department selects 10 at random (from the 40 produced) for testing and
will shut down the plant for trouble shooting if 1 or more in the sample are found to be
defective. What is the probability that the plant will be shut down? (Exercise 76, Page
397)
Dr. Glenn Rice
Section 8.2: Union, Intersection, and Complement of Events
MWSU
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