Probability Rules!!! Section 5.2 Reference Text: The Practice of Statistics, Fourth Edition....
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Transcript of Probability Rules!!! Section 5.2 Reference Text: The Practice of Statistics, Fourth Edition....
Probability Rules!!!
Section 5.2
Reference Text:
The Practice of Statistics, Fourth Edition.
Starnes, Yates, Moore
Objectives1. 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 ModelsSome 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 AEvent A P(A) = 90/178P(A) = 90/178
Event BEvent B P(B) = 103/178P(B) = 103/178
P(A and B) = 19/178P(A and B) = 19/178
Venn DiagramGeneral 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
Objectives1. 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!
• 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)• Ch. 1 Test Ch. 2 Test Ch. 3 Test Ch. 4 Test• A 5 A 5 A3 A1• B5 B 6 B5 B9• C6 C 4 C6 C3• D2 D 1 D2 D5• F1 F 2 F2 F1
Homework
Worksheet