daniel meissner nick lauber kaitlyn stangl lauren desordi
Post on 13-Jan-2016
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If event E1 can occur m1 different ways and event E2 can occur m2 different ways then the number of ways they can both occur is m1 * m2
Equation for total possible outcomes:m1 * m2…. *mk
Fundamental Counting Principle
An arrangement of objects where order matters
n! = Number of permutations of n objects
nPr = Number of permutations of n objects taken r at a time
Permutations
If a set of n objects has n1 of one kind, n2 of another kind etc…
The number of distinguishable permutations
Distinguishable Permutations
!n!...n!n!n
!
k321 n
An arrangement where order does not matter
nCr: Number of combinations of n objects taken r at a time
Combinations
A happening for which the results is uncertain1. Outcomes: Possible results2. Sample Space: The set of all possible
outcomesa) Event: A subset of the sample space
Experiment
If an event E has n(E) equally likely outcomes and its sample space s has s(E) equally likely outcomes then the probability of event E is
Compliments: The probability that event E will not happen
P(E’) = 1 – P(E)
Probability
)(
)()(
Es
EnEP
Events in the same sample space that have no common outcomes:
P(A n B) = 0
If A and B are 2 events in the same sample space, then the probability of A or B is
P(A u B) = P(A) + P(B) – P(A n B)
If A & B are mutually exclusive, then just
P(A u B) = P(A) + P(B)
Two events are independent if the occurrence of one event has no effect on the occurrence of the other event
Compound Probability
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