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71 Cards in this Set

  • Front
  • Back
What is a factorial?
For a positive integer n we define n factorial as n∙(n-1)∙(n-2)∙...∙3∙2∙1

denoted n!
What are the two basic principles of counting?
The Rule of Sum

The Rule of Product
What is the Rule of Sum?
If a first task can be performed in m ways and a second task can be performed in n ways and the two tasks can not be performed at the same time, then performing either task can be accomplished in any way of m+n ways.
What does it mean when two tasks can not be performed at the same time?
They are mutually exlusive.
What if the tasks are not mutually exlusive?
When we have two tasks A and B, the number of ways to perform either task is n(A)+n(B)-n(A⋂B)
What is the Rule of Product?
If a procedure can be broken down into first and second stages and if there are m possible outcomes for the first stage and from each of those outcomes there are n possible outcomes for the second stage, then the total procedure can be carried out, in the designated order, in mn ways.
What is an r-permutation?
An ordered sequence of r objects from the set X.
How do we define P(n,r)
The number of r-permutations chosen from n objects.
How do we calculate P(n,r)
What is an r-combination?
An unordered selection of r objects chosen from the set X.
What is C(n,r)?
The number of r-combinations of n elements.
How do we find C(n,r)?
How do we express probability?
A ratio describing the number of favourable occurences to the number of total possible occurences for some specified result of an observable event.
What is empirical probability?
Probability that is determined on the basis of conducting an experiment or examining data
What is the sample space?
The set of all possible outcomes
How do we find the empirical probability of an experiment?
An experiment with a number of possible outcomes is peformed n times. If event E occurs r times, the empirical probability, denoted Pe(E), says that E will occur on any given trial of the experiment is Pe(E)=r/n
What is the Law of Large Numbers?
If an experiment is performed repeatedly the empirical probability of a particular outcome more and more closely approximates a fixed number as the number of trials increases.
When are outcomes equally likely?
If each outcome of an experiment is as likely to occur as any other outcome
What is the probability of an event E, if all outcomes are equally likely?
P(E) = number of outcomes in E / number of outcomes in sample space

P(E)= n(E)/n(S)
What values must P(E) fall between?
What does it mean if P(E)=0?
Event E is impossible
What does it mean if P(E)=1?
Event E will always happen
What is the probability of E compliment?
E compliment (denoted E bar) is 1-P(E)
If A and B are mutually exclusive events, how do we find P(A or B)?
P(A or B) = P(A) + P(B)
If A and B are not mutually exclusive events, how do we find P(A or B)?
P(A or B) = P(A) + P(B) - P(A and B)
If A and B are independant events, how do we find P(A and B)?
P(A and B) = P(A) x P(B)
What does P(A|B) mean?
Find the probability of event A given that event B has already occured.
How do we find P(A|B)?
P(A|B) = P(A and B)/P(B)
What is odds in favour of an event?
The ratio of the number of favorable outcomes to unfavorable outcomes.
How can we find odds in favor of event E?
n(E):n(not E)
How can we find the odds in favor of E using probability?
P(E):P(not E)
If the odds in favor of E are a:b what is P(E)?
P(E)= a/(a+b)
What is expected value?
The long-run average value over repeated plays of a payoff from a game or event
How do we find the expected value?
If the outcomes of an experiments have values V1, V2, V3...Vn then the expected value is P1V1 + P2V2 +...+PnVn
What is a point?
A location in space that does not have length, width, or height.

We represent points with a dot, and label them with capital letters.
What is a line?
A set of points in a straight unlimited length with no thickness or endpoints.

Any two points determine one and only one line. We denote the line formed by points A & B as AB with a line (<->) above it
What are collinear points?
Two or more points on the same line are collinear.
What is the plane?
A set of points in a flat surface that has no thickness and no edges
What is a line segment?
Two points on a line and all the points between them; it has a definite start and end point.

We denote the line segment between points A & B as AB with __ above it
What does it mean to bisect a line segment?
To divide the line into 2 parts of equal length.
What is the midpoint?
The point that bisects the line.
What are congruent lines?
Lines that have the same length.

Denoted with ≅
What are parallel lines?
Two lines in the plane are parallel if they have no points in common.

Denoted l || m

If two lines are not parallel, they MUST intersect at some point
Where do lines intersect?
At the point of intersection
What are concurrent lines?
Three lines that intersect at the same point
What is a ray?
The ray AB is point A and all the points on line AB that are on the same side of A as B is

Denoted AB with -> overtop
How is an angle formed?
When two rays or line segments have a common end point.

Denoted with ∠
What is the vertex?
The common endpoint of the angle.

In ∠BAC A is the vertex
How do we find the measure of the angle?
We find the amount of rotation. Denoted m(∠BAC), measured in degrees

How many angles are formed by two rays?
Two - the interior angle and the exterior angle
What does ∠BAC usually refer to?
The smaller of the two angles (the interior) so m(∠BAC)≤180
What is a zero angle?
When the angle measures 0
What is an acute angle?
When the angle measures less than 90
What is a right angle>?
When the angle measures 90
What is an obtuse angle?
When the angle measures between 90 and 180
What is a straight angle?
When the angle measures 180
What is a reflex angle?
When the angle measures between 180 and 360
What are perpendicular lines?
Two lines that intersect to form 4 90 degree angles.

Denoted l⊥m
What are congruent angles?
Two angles that have the same measure.
What are complementary angles?
Angles whose measures add up to 90
What are supplementary angles?
Angles whose measures add up to 180
What are adjacent angles?
Two angles that have hte same vertex and a common side, but no common interior points.
What are linear angles?
Angles that are adjacent and have two non-common sides on the same line
What are vertical angles?
Angles formed by two intersecting lines, that are not a linear pair of angles
What is a transversal?
A line that intersects two other lines
What are corresponding angles?
Two non-adjacent angles on the same side as the transversal, one interior and one exterior
What can we say about the corresponding angles if the two lines cut by a transversal are parallel?
They are congruent
What are alternate interior angles?
Two non-adjacent interior angles on opposite sides of the transverasl, forming a Z

Alternate interior angles are congruent
What does the Alternate Interior Angle Theorem say?
Two lines cut by a transversal are parallel if and only if a pair of alternate interior angles are congruent.
What is the angle sum of triangles?
The sum of the measures of the interior angles of a triangle is 180