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5.2 Combining Events
Objectives:By the end of this section, I will beable to…
1) Understand how to combine events using complement, union, and intersection.
2) Apply the Addition Rule to events in general and to mutually exclusive events in particular.
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Complements
What is P(4) with one die?
What is P(not 4) with one die?
These are considered complementary events.
𝟏𝟔𝟓𝟔
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Complements
If one event is called Event A, the complement is called Ac.
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SINGLE EVENTS
What is the p(face card) from a standard deck of cards?
What is the p(hearts) from a standard deck of cards?
12/52
13/52
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COMBINING EVENTS
What is the p(face cards and hearts)?
Make a Venn Diagram
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FACE CARDS
HEARTS
Face Cards
& Hearts
SAMPLE SPACE (everything else)
Event A = Face cardsEvent B = Hearts
P(A) = P(A) = 12/52P(B) =P(B) = 13/52P(A and B) = P(A and B) =
3/52P(A or B) = P(A or B) =
22/52
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Probability NotationShorthan
d Notation Written OutVenn Diagram
not A Ac Complement of A
A and B
A ∩ B
Intersection of A and
B
A or B
A U B
Union of A and B
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Mutually Exclusive Events
Two events, A and B, that cannot occur at the same time.
Example: Fly a plane and drive a car at the same time (its impossible!)
KEY WORDS: OR, EITHER
p(A or B) = p(A) + p(B)
p(A U B) = p(A) + p(B)
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Spoiled Brats
Tankle has been shopping around for a new HOT ROD!! The probability a customer will buy an JEEP is 0.23 and the probability that a customer will buy a BMW is 0.09.
What is the probability that Matt will buy EITHER of these two Cars?0.23 + 0.09 =
0.32
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CRAPS Two dice are rolled. What is the
probability that the sum of the dots is a 7 OR 11?
6/36 + 2/36= 8/36
= 0.22
4,3 3,4 2,5 5,2 1,6 6,1
5,6 6,5
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OVERLAPPING Events Addition Rule:
p(A or B) = p(A) + p(B) – p(A and B)
SUBTRACT OUT THE OVERLAPPING PART OF THE EVENT!
What is the p(Ace or Hearts)?𝟒𝟓𝟐
+𝟏𝟑𝟓𝟐
−𝟏𝟓𝟐
𝟏𝟔𝟓𝟐
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CARDS
WHAT IS THE PROBABILITY OF SELECTING A RED CARD OR A KING FROM A STANDARD DECK OF CARDS?26/52 + 4/52 – 2/52 = 28/52 = 0.53846 = 0.54
26/524/52
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Try This One!
The probability of a guard being chosen by Coach Godfrey to start the basketball game is 0.42 and the probability that she chooses a forward is 0.34.
Three out of every five players can play both positions on Coach Godfrey’s team.
What is the probability that a player chosen to start the game is a guard OR a forward?
0.42 + 0.34 - 3/5 =
0.16