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35 Cards in this Set
- Front
- Back
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probability
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the chance of an event occurring
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probability experiment
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a chance process that leads to well defined results called outcomes
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outcome
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the result of a single trial of a probability experiment
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sample space
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the set of all possible outcomes of a probability experiment
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event
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a set of outcomes of a probability experiment
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simple event
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event with one outcome
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compound event
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consists of two or more outcomes or simple events
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the three basic interpretations of probability
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1) classical probability
2)empirical or relative frequency probability 3)subjective probability |
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classical probability assumes...
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that all outcomes in the sample space are equally likely to occur
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formula for classical probability
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the probability of any event "E" is
(number of outcomes divided in E)/ (total number of outcomes in sample space) |
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in what ways can probabilities be expressed?
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as fraction, decimals and sometimes percentages
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rounding rule for probabilities
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should be expressed as reduced fractions or rounded to two or three decimal places
for very small probability round to the nearest non zero .0000578=.00006 |
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four basic probability rules
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The sum of probabilities of the outcome in a sample space it 1.
If an event "E" is certain, the probability of "E" is 1. If an event "E" cannot occur, the probability is 0. The probability of event "E" is between and including 0 and 1. |
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the complement of event "E" is shown by...
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E "bar"
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Venn diagrams represent
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probabilities pictorially
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empirical probability
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relies on actual experience or observation to determine the likelihood of outcomes
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Formula for empirical probability
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f/n
where f=frequency for class n=total frequencies in the distribution |
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the law of large numbers
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as the number of trials increase the empirical probability will approach the theoretical probability
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subjective probability
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uses opinions and inexact information
(educated guesses) |
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mutually exclusive events
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cannet occur at the same time, they have no outcomes in common
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when "A" and "B" are mutually exclusive the probability that "A" or "B" will occur is
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P(A)+P(B)
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when "A" and "b" are NOT mutually exclusive the probability is found by
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P(A)+P(B)-P(A and B)
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independent events
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do not effect the probability of another event occurring
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rule for two independent events both occurring
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P(A)+P(B)
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dependent events
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if the outcome or occurrence of one event effects the outcome or occurrence of another
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for dependent events the probability of both occurring is
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P(A)*P(B/A)
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conditional probability
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the probability of event "B" occurring after event "A"
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formula for conditional probability
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P(A and B)/P(A)
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0!=
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1
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permutation
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an arrangement of objects in a specific order
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Permutation rule
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nPr = n!/(n-r)!
n= objects r= objects at a time |
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combination
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selection of objects without regard to order
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combinations are used when
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the order of arrangement is not important
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combination rule
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nCr = n!/(n-r)!r!
n= objects r= objects at a time |
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fundamental counting rule (define)
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the number of ways a sequence of "n" events can occur if the first event can occur K 1 ways, the second can occur K 2 ways, etc.
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