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20 Cards in this Set
- Front
- Back
- 3rd side (hint)
Addition Rule for Disjoint Events
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If events A, B, and C are disjoint in the sense that no two have any outcomes in common, then
P(A or B or C)=P(A)+P(B)+P(C) |
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General Addition Rule for Unions of Two Events
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For any two events A and B,
P(A or B)=P(A)+P(B)-P(A and B) |
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Simulation
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Imitation of chance behavior, based on a moedl that accurately reflects the phenomenon under consideration
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Randint Function
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randint(x,y,z)
x=minimum y=maximum z=number of digits to generate |
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Simulation Steps
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State problem or describe random phenomenon
state assumptions assign digits simulate many repetitions state conclusions |
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Empirical
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Based on observation, not theory
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Probability Models
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Sample space S of a random phenomenon is set of all possible outomes
event is any outcome or set of outcomes of a random phenomenon probability model is mathematical description of a random phenomenon, consisting of a sample space and a way of assigning probabilities to events |
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Tree Diagram
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A handy way to depict all possible outcomes
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Multiplication Principle
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if you can do something n ways and another m ways, the total number of ways to do both is n x m
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Sampling with replacement
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Put the things back after drawing
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Sampling without replacement
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Not putting things back after drawing them
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probability rules
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any probability is between 0 and 1
the sum of all probablities of all possible outcomes must equal 1 if 2 events have no outcomes in common, the probability that one or the other occurs is the sum of the two individuals the probability that an event does not happen is 1 minus the probability that the event does occur |
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Mickey Rat
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RATS
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Venn Diagram
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diagram to find probability of union of two events or joint probability
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Disjoint events
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probability of A and B is 0
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Conditional Probability
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Complement (A^c)
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i.e. complement of Event A is all outcomes that are not in A
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Random Phenomenon
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Outcomes that we cannot predict but that nonetheless have a regular distribution in very many repetitions.
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Total Probability
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All of the probabilities must add up to 1.
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P(S) = 1
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Joint Probability
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The probability of two events occurring together.
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