Statistics Chapter 4
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15 Terms
1
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mutually exclusive
* Will NOT happen at the same time
* ex. “hot or cold?”
* could be dependent (A could affect if B happens or not)
* P\[A\] + P\[B\]= Probability of A **OR** B
* ex. “hot or cold?”
* could be dependent (A could affect if B happens or not)
* P\[A\] + P\[B\]= Probability of A **OR** B
2
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not mutually exclusive
* some data overlap
* ex. “rainy or sunny (or both)?”
* P\[A\] + P\[B\]- P\[A and B overlap\]= Probability of A **OR** B
* ex. “rainy or sunny (or both)?”
* P\[A\] + P\[B\]- P\[A and B overlap\]= Probability of A **OR** B
3
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dependent
* Influences the other (“Conditional Probability”)
* ex. outside temperatures→ public pool attendance
* P\[A\] × P\[B|A\]= Probability of A **AND** B
* "Probability of B given that A occured”
* ex. outside temperatures→ public pool attendance
* P\[A\] × P\[B|A\]= Probability of A **AND** B
* "Probability of B given that A occured”
4
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independent
* A occurring/not occurring does not change the probability of B
* ex. outside temperatures → money spent on school supplies
* P\[A\] × P\[B\]= Probability of A **AND** B
* ex. outside temperatures → money spent on school supplies
* P\[A\] × P\[B\]= Probability of A **AND** B
5
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Permutation Rule
* Order **IS** important!
* nPr=n!/(n-r)!
* n= number of objects
* r= number of spots
* “how many ways can x objects be organized by size?”
* nPr=n!/(n-r)!
* n= number of objects
* r= number of spots
* “how many ways can x objects be organized by size?”
6
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Combination Rule
* Order **IS NOT** important!
* nCr=n!/(n-r)! × r!
* n= number of objects
* r= number of spots
* “how many ways can this office with y spots be filled by x people?”
* nCr=n!/(n-r)! × r!
* n= number of objects
* r= number of spots
* “how many ways can this office with y spots be filled by x people?”
7
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3 Types of Probability
* Theoretical/Classical
* equally likely events
* what **should** happen give past data/knowledge
* Experimental/Empirical
* what **does** happen
* current data/knowledge
* Subjective
* opinion
* unimportant to Mr. Cutler
* equally likely events
* what **should** happen give past data/knowledge
* Experimental/Empirical
* what **does** happen
* current data/knowledge
* Subjective
* opinion
* unimportant to Mr. Cutler
8
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3 (1/2) Rules of Probability
1. The probability of an event is going to be 0-1 ALWAYS
2. Sum of every event’s probability must add up to 1
3. The probability of an event NOT occurring is 1-P(event)
3 1/2. Round everything to three or four decimal places. 0 ≠ 0.0000.
9
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complement
* The probability of an event NOT occurring. The opposite.
* “The complement to all spots being filled by x is having **at least one spot** being filled by y.”
* “The complement to all spots being filled by x is having **at least one spot** being filled by y.”
10
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probability
the chance of an event occurring
11
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probability experiment
the process in which events occur
12
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outcome
result of a single trial of a probability experiment
13
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sample space
all possible outcomes of an experiment
14
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equally likely events
every sample space outcome has the same probability
15
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Law of Large Numbers
If a probability experiment is performed a lot, you should theoretically get the same answers for the empirical and the classical hypotheses
* The “should be” = “has been”
* The “should be” = “has been”