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(Ch. 14) GRE Counting Methods and Probability Review
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Terms in this set (16)
Sets
groups of values that have some common property; all the elements are unique; order does not matter; can be finite or infinte; are enclosed in curly brackets { }
Ex. 1, 1, 2, 2, 3 is {1, 2, 3} and the same as {3, 2, 1}
Lists
like a finite set except *the order of elements matters and duplicate members can be included.* So elements can be uniquely identified by their position (ex. 1st element, 5th element). Not enclosed in curly brackets
Intersection of sets
the elements that are common to two or more sets. The intersection of sets A and B is written as A∩B.
Union of sets
the set of all elements that are elements of either or both sets and is written as A∪B
Mutually exclusive sets
When sets have no common elements; their intersection is the empty set
Universal set
the universal set is the set of all elements considered in a particular problem U; represented in a Venn diagram.
# of elements in the union of two sets formula
|A∪B|=|A|+|B|-|A∩B|
Multiplication Principle
When choices or events occur one after the other and the choices or events are independent of one another, the total number of possibilities is the product of the number of options for each.
ex. How many different ways can a voter fill out a ballot if Office A has 3 choices, Office B has 4 choices, and Office C has 2 choices?
3 x 4 x 2 = 24 different ways.
Combination
How many unordered subgroups can be formed from a larger group.
*order does not matter*
Formula: n! / r!(n-r)!
n = # of items in the group as a whole
r = # of items in each subgroup formed
! = factorial (ex. 3! = (3)(2)(1)= 6)
Permutation
The possible multiple arrangements within any group. *order matters*
Formula: n! / (n-r)!
n = # of items in the group as a whole
r = # of items in each subgroup formed
! = factorial (ex. 3! = (3)(2)(1)= 6)
Probability
measures the likelihood that an event will occur.
P(E) =
# of desired outcomes / # of possible outcomes
Probability of not occurring
1 - P(E)
Probability of Multiple Events (independent)
To calculate the probability of two or more independent events occurring, multiply the probabilities of the individual events.
P₁+₂ = P₁ X P₂
Probability of multiple events (dependent)
Multiply the probability of the two dependent events, but the probabilities will be different (unlike in independent events)
Ex. What is the probability of drawing 2 red marbles from a bag of 10 with 4 blue and 6 red?
P₁ = (6/10), then the second probability you will have 1 less marble overall and 1 less red marble, so (5/9).
(6/10)(5/9) = 1/3
Formula for overlapping sets (crossover problems)
Total = Group A + Group B - Both + Neither
Probability of one event or another occurring
P₁ or ₂ = P₁ + P₂ - P(overlap)
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