Probability
Terms
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- Define 'Random'
- Random if individual outcomes are uncertain but there is nonetheless a regular distribution of outcomes in a large number of repetitions
- Define 'Probability'
- The proportion of times an outcome would occur in a very long series of repetitions.
- Define 'Sample space "S"'
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The set of all possible outcomes.
ex: S={1,2,3,4,5,6,7} - Deinfe 'probability model'
- For a random phenomenon, consists of a sample space 'S' and an assignment of probabilities 'P'.
- Define 'Compliment'
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For event A, the compliment consists of exactly the outcome NOT in A.
ex: if P(A)=80%, then P(A Compliment)=20% - Define 'Disjoint'
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Events A and B are disjoint if they have NO outcomes in common.
(**Do NOT confuse this with independence! Events _can_ be both disjoint and dependent, even though it rarely happens**) - Define 'Independent'
- Knowing that one event occurs does not change the probability we would assign to the other event.
- Addition Rule for disjoint events
- P(A or B) = P(A) + P(B)
- Multiplication rule for independent events
- P(A and B) = P(A) x P(B)
- Compliment rule
- P(A Compliment) = 1 - P(A)
- Define 'Union'
- For events A and B, contains all of the outcomes in both A and B.
- Define 'intersection'
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The events that ALL of the events occur together.
ex: Out of 100 people, 80 people took STATS, 30 people took Psychology, and thus 10 people took STATS and Psychology (this is an intersection). - How do you know if events are independent?
- In terms of conditional probability, events are ndependent if P(A/B) = P(B)
- Conditional Probability
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This si the probability of one event under the condition that we know another event.
Ex: Give the % of students who are enrolled in AP Statistics given that they are female.
The multiplication rule for the union of two events in terms of conditional probability is:
P (B/A)= P(A) x P(B/A), where B"/"A means B "given" A.
The definition of conditional probability when P(A) > 0 is:
P(A/B)= P(A and B)
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P(A)