Reading...
Play button
Play button
Use LEFT and RIGHT arrow keys to navigate between flashcards;
Use UP and DOWN arrow keys to flip the card;
H to show hint;
A reads text to speech;
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)
|
P(n,r)=n∙(n-1)∙(n-2)∙...∙(n-r+1)
OR n!/(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)?
|
C(n,r)=n!/[r!∙(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?
|
0≤P(E)≤1
|
|
|
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
0<m(∠BAC)<360 |
|
|
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
|
