Int2 Ch03 CPM

Delta (Δ)

A Greek letter that is often used to represent a difference, or change, in values. Its uses include Δx and Δy, which represent the lengths of the horizontal and vertical legs of a slope triangle, respectively.

Theta (θ)

A Greek letter that is often used to represent the measure of an angle. Other Greek letters used to represent the measure of an angle include alpha (α) and beta (β).

Clinometer

A device used to measure angles of elevation and depression.

Probability Area Model

A model that uses the area of rectangles to represent the probabilities of possible outcomes when considering two independent events.

Tree Diagram

A model used to organize the possible outcomes and the respective probabilities of two or more events.

Slope Ratio

Change in y over change in x. (Δy/Δx) This can also be used to find the tangent ratio.

Fair Game

For the purposes of this course, a fair game has an expected value of 0 for all players. Therefore, over many plays, any player would expect to neither win nor lose points or money by playing a fair game.

Expected Value

For this course, the expected value of a game is the average amount expected to be won or lost on each play of the game if the game is played many times. Expected value can be found by summing the probability of each outcome multiplied by its value.

Independent Events

If the outcome of a probabilistic event does not affect the probability of another event, the events are independent. For example, assume you plan to roll a normal six‑sided die twice and want to know the probability of rolling a 1 twice. The result of the first roll does not affect the probability of rolling a 1 on the second roll; the events are independent.

Tangent Ratio

In a right triangle, the tangent ratio of an acute angle A, is tan(A) = length of opposite side/length of adjacent side.

Trigonometry

Literally means the "measure of triangles". In this course, this word is used to refer to the development of triangle tools such as trigonometric ratios (sine, cosine, and tangent) and the Laws of Sines and Cosines.

Event

One or more results of an experiment or probabilistic situation.

Addition Rule for Probability

P(A or B) = P (A) + P (B) - P(A and B)

Slope Angle

The acute angle a line forms with the x-axis on a coordinate graph.

Intersection of two events

The intersection of the two events {A} and {B} is a new event that includes all the outcomes in which both A and B will occur. For example, if event {A} is the thirteen diamond‑suited cards in a deck of playing cards, and {B} is the four Aces, then the event {A intersection B} contains 1 outcome: {A♦}.

Probability

The probability that an event A, with a finite number of equally likely outcomes, will occur is the number of outcomes for event A divided by the total number of equally likely outcomes. A probability p is a ratio, 0 ≤ p ≤ 1.

Sample Space

The set of all possible outcomes.

Complement of an Event

The set of all the outcomes in the sample space that are not in the event. For example, if you randomly select one card from a deck of cards, the event {the card is a diamond} has a probability of 13/52. The complement of the event is {the card is not a diamond} or {the card is a heart, spade, or club}, and has a probability of 1 − 13/52 = 39/52.

Legs of a right triangle

The two sides of a right triangle that form the right angle. Note that the legs of a right triangle are always shorter than its hypotenuse.

Union of two events

The union of the two events {A} and {B} is a new event that includes all the outcomes that either A will occur or B will occur. For example, if event {A} is the thirteen diamond-suited cards in a deck of playing cards, and {B} is the four Aces, then the event {A union B} contains 16 outcomes: {all the diamonds (including the A♦), A♥, A♣, and A♠}. NOTE: You use the addition rule to solve for the union of two events!