Probability Rules!!!
Section 5.2
Reference Text:
The Practice of Statistics, Fourth Edition.
Starnes, Yates, Moore
Objectives
1. Probability Models
– Sample Space -Probability Model
- Event
2. Basic Probability Rules
– Compliment “not A”
-Mutually exclusive (disjoint)
3. Addition Rule
– P(A or B) =P(A) + P(B)
4. Two way tables
5. Venn Diagrams
– Intersections and Unions.
Probability Models
Some lingo to get down
• Toss a coin. What are the possible outcomes?
• A: Heads or tails! This is what's know as our
sample space
• Roll a regular 6-sided die. What are the possible
outcomes?
• ____ ____ _____ _____ ____ ____
• Probability model: some chance process that
consists of two parts: Sample space S, and
probability for each one…. Lets look at rolling
two 6-sided die! What are the outcomes?
Events
• With the two dice rolled, we could find any
collection of outcomes and their
probabilities.
• This is what’s known as an Event- any
collection of outcomes from some chance
process. Events are assigned capital
letters such as A,B,C
• P(A) where A= sum of 5.
Compliment
Lets try some more!
•
•
•
•
A = sum of 5
B = sum is not 5
C = sum is 6
Find the probability of the following:
P(A)=
P(B)=
P(C)=
P(A or C)=
- Notice how P(A) +P(B) = 1
Basic Rules of Probability
Mutually Exclusive
(disjoint)
• Two events are mutually exclusive if they
have no outcomes in common and so can
never occur together.
• Example: if one event occurs in 40% of all trials,
and a different event occurs in 25% of the trials,
and the two can never occur together, then one
or the other occurs on 65% of the trials.
40% + 25% = 65%
Check for Understanding
• Chose an American adult at Random. Define two events:
A = the person has a cholesterol level of 240 milligrams per
deciliter of blood (mg/dl) or above. (High cholesterol)
B= The person has a cholesterol level of 200 to 239
(borderline high cholesterol)
• According to the American Heart Association:
P(A) = 0.16 and P(B) = 0.29
1. Explain why events A and B are mutually exclusive.
2. Say in plain language what the event “A or B” is. What is
P(A or B)?
3. If C is the event that a person chosen has normal
cholesterol (below 200 mg/dl) what's P(C)
Two way Tables
• Students in college stats class wanted to find out
how common it is for young adults to have their
ears pierced. They recorded data on two
variables- gender and whether the student had a
pierced ear – for all 178 people in class. The two
way table below displays the data.
Pierced ears?
Gender
Yes
No
Total
Male
19
71
90
Female
84
4
88
Total
103
75
178
A= male B= pierced ears
• Suppose we chose a student from the class at
random. Find the probability that the student
• (a) has pierced ears
• (b) is a male with pierced ears
• (c) is male or has pierced ears
Venn Diagrams
Event A
P(A) = 90/178
Event B
P(B) = 103/178
P(A and B) = 19/178
Venn Diagram
General Addition Rule
• The Venn Diagram suggests to fix this
“double counting”
• P(A or B) = P(A) + P(B) – P(A and B)
= 90/178 + 103/178 – 19/178
= 174/178
Intersection and Unions
• If we are talking about “A and B” then we
can also call this the intersection of A and
B. The corresponding notation is A П B
• If we are talking about “A or B” then we
can also call this the Union of A and B.
The corresponding notation is A U B
Venn Diagram: Intersection and
Unions
Objectives
1. Probability Models
– Sample Space -Probability Model
- Event
2. Basic Probability Rules
– Compliment “not A”
-Mutually exclusive (disjoint)
3. Addition Rule
– P(A or B) =P(A) + P(B)
4. Two way tables
5. Venn Diagrams
– Intersections and Unions.
Test Results!
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•
•
•
•
•
Grade:
Amount: Marginal %
……A......……....1.……….5%
…….B…………...9……...47% 68% Passed
…….C…………..3..……...16%
…….D…………..5.……...26%
…….F…..............1………..5% 31% Failed
• Mean: 79% Max: 92% Min: 58% No Outliers
Tracking AP Stats
• 2014-2015 (WHS)
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Ch. 1 Test Ch. 2 Test
A5
A5
B5
B6
C6
C4
D2
D1
F1
F2
Ch. 3 Test Ch. 4 Test
A3
A1
B5
B9
C6
C3
D2
D5
F2
F1
Homework
Worksheet