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18 Cards in this Set
- Front
- Back
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Multiplication Counting Principle
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if one event can occur in “m” ways and another event can occur “n” ways, then the number of ways that BOTH can occur TOGETHER is “(m)(n)”. This principle can be extended into three or more events. (BOTH ..this one “AND” that one)
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Addition Counting Principle
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if the possibilities being counted can be divided into groups with no possibilities in common, then the total number of possibilities is the SUM of the numbers of possibilities in each group. (One “OR” the other, but not both)
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Probability
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is the ratio of the number of outcomes in the event to the total number of outcomes in the sample space – it is the likelihood that an event will occur
P(E) = # of possible in event/total |
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Sample Space
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the set of all possible outcomes
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Factorial Notation
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is indicated by the “!” symbol. The expression n! is read “n factorial” and means to multiply “n” times “(n-1)!” or “n! = n(n-1)!” The expression 0! = 1 (example: 5! = 5x4x3x2x1 = 120)
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Permutation
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is an ordering of a set of objects. When you are concerned with how objects in a set are ordered, you should determine the number of permutations. (examples: 1st, 2nd place; President,Vice President; 1st and 2nd chair – order matters)
Formula: n!/(n-r)! n= number of objects r = taken "r" at a time |
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Combination
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a selection of objects where the order of the objects is not important – combinations are used to count possibilities (examples: order a “set of”, combinations for a “group of”, co-captains, co-chairs)
Formula: n!/(n-r)!r! |
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Compound Event
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two or more events, using the word “and” or the word “or”
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“or” probability
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ADD the probabilities – the events are either a)mutually exclusive b)Overlapping
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Mutually Exclusive Events
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an “or” compound event in which there are no common outcomes
P(A and B) = P(A) + P(B) |
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Overlapping Events
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an “or” compound event in which at least one common outcome exists
P(A and B) = P(A) + P(B) – P(A and B) |
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“and” probability
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– MULTIPLY the probabilities – the events are either a)independent b)dependent
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Independent Events
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an “and” compound event in which the occurrence of one event has no effect on the occurrence of the other (examples – drawing “with replacement”, spinners, rolling a die)
P(A and B) = P(A) P(B) |
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Dependent Events
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and “and” compound event in which the occurrence of one event affects the occurrence of the other (examples – drawing “without replacement”)
P(A and B) = P(A) P(B given A) |
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Expected Value
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the sum of the products of the events’ probabilities and their values
Steps: 1) find the probability of each possible outcome (they should add to get 1) 2)multiply each probability by its value 3)take the sum of those products |
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Complement
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the probability of the event not occurring P(A^c ) = 1 – P(A)
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Fair
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getting the outcome one would expect
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Random
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events are random when individual outcomes are uncertain
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