daniel meissner nick lauber kaitlyn stangl lauren desordi
TRANSCRIPT
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