Danny Lee
Professor James W. Chaires
Math 221
Chapter 5 Definitions
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Experiment: An activity or measurement that results in an outcome
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Sample Space: All possible outcomes of an experiment.
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Event: one or more of the possible outcomes of an experiment; a subset of the sample space.
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Probability: a number between 0 and 1 which expresses the chance that an event will occur.
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Classical probability: For outcomes that are equally likely,
Probability = Number of possible outcomes in which the event occurs, divided by the total number of possible outcomes
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Relative frequency probability : For a very large number of trials.
Probability = Number of trials in which the event occurs, divided by the total number of trials.
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Subjective probabilities : Where the subjective approach to probability is judgmental, representing the degree to which one happens to believe that an event will or will not happen,( hunches or educated guesses).
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Odds: A way of expressing the likelihood that something will happen.
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Mutually exclusive events: If one event occurs the other cannot occur. An event
(e.g., A) and it’s compliment ( A’) are always mutually exclusive.
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Exhaustive Events : A set of events that includes all the possible outcomes of an experiment.
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Intersection of Events : Two or more events occur at the same time.
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Union of Events : At least one of a number of possible events occurs.
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Addition rules for probability : Occasions where we wish to determine the probability that one or more of several events will occur in an experiment.
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Rule of addition when events are mutually exclusive : P(A or B) = P(A) + P(B)
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General rule of addition when events are not mutually exclusive : P(A or B) =
P(A) +P(B) – P(A and B)
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Marginal Probability : The probability that a given event will occur. No other events are taken into consideration.
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Joint Probability : The probability that two or more events will all occur.
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Conditional Probability : The probability that an event will occur, given that another event has already happened.
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Independent events : When the occurrence of one event has no effect on the probability that another will occur.
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Dependent events: When the occurrence of one event changes the probability that another will occur.
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Multiplication rule when events are independent :
P(A and B) = P(A) P(B)
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Multiplication rule when events are not independent :

P(A and B) = P(A) x P(B\A)
 Bayes’ Theorem for the revision of probability
:
1.
Events A and B: Probability of A, given that event B has occurred:
P(A\B) = P(A and B) / P(B) = P(A) * P(B\A)
--------------------------------------------
P(A) * P(B\A)] + [P(A’) * P(B\A’)

Factorial : In which the product (5 x 4 x 3 x 2 x 1) can be described as 5!. For example, 3! Is the same as 3 x 2 x 1. The exclamation point is just a mathematical way of saving space.
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Permutations: refers to the number of different ways in which objects can be arranged in order.
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Combinations : Unlike permutations, combinations consider only the possible sets of objects, regardless of the order in which the members of the set are arranged.