2A-2D Probability Unit Vocab

Quiz on Oct. 1!

two-way table

a table of counts or relative frequencies that summarizes data on the relationship between two categorical variables for some group of observational units.

marginal relative frequency

gives the percentage or proportion of observational units in a two-way table that have a specific value for one categorical variable. A marginal relative frequency is calculated by dividing a row or column total by the total for the entire two-way table.

joint relative frequency

gives the percentage or proportion of observational units in a two-way table that have a specific value for one categorical variable and a specific value for the other categorical variable. A joint relative frequency is calculated by dividing the value in one cell by the total for the entire two-way table.

conditional relative frequency

gives the percentage or proportion of observational units that have a specific value for one categorical variable among a group of observational units that share the same value of another categorical variable (the condition). A conditional relative frequency is calculated by dividing the value in one cell of a two-way table by the total for the appropriate row or column.

segmented bar chart

displays the distribution of a categorical variable as segments of a bar, with the area of each segment proportional to the number of observational units in the corresponding category. There is a separate bar for each group, corresponding to the values of another categorical variable.

mosaic plot

is a modified segmented bar chart in which the width of each bar is proportional to the number of observational units in the corresponding category.

Association

between two variables if knowing the value of one variable helps us predict the value of the other. If knowing the value of one variable does not help us predict the value of the other, there is no association between the variables.

random process

generates results that are determined purely by chance

outcome

the result of one trial of a random process

event

a subset of the possible outcomes from a random process

probability

of any outcome or event from a random process is a number between 0 and 1 that describes the proportion of times the outcome or event would occur in a very long series of trials.

Law of Large Numbers

says that if we observe more and more trials of any random process, the proportion of times that a specific outcome or event occurs approaches its probability.

Simulation

imitates random behavior in such a way that simulated outcomes are consistent with real-world outcomes.

probability model

is a description of a random process that consists of two parts: a list of all possible outcomes and the probability of each outcome.

sample space

the list of all possible outcomes

P(A)

=number of outcomes in event A/total number of outcomes in sample space

Basic Probability Rules (Fill in the blank—no word bank.)

(1) The probability of any event is a number between 0 and 1, inclusive
(2) All possible outcomes in the sample space must have probabilities that add up to 1
(3) The probability that an event does not occur is 1 minus the probability that the event does occur.

Complement Rule

says that P(AC) = 1 -P(A), where AC is the complement of event A-that is, the event that A does not occur.

Complement

the set of all outcomes in the sample space that are not in that event

mutually exclusive

two events A and B are _____ if they have no outcomes in common and so car never occur together—that is, if P(A and B) = 0

Addition Rule for Mutually Exclusive Events

A and B says that P(A or B) = P(A) + P(B)

General Addition Rule

If A and B are any two events resulting from the same random process, _____ says that P(A or B) = P(A) = P(B) = P(A and B)

Venn diagram

consists of one or more circles surrounded by a rectangle. The region inside the rectangle represents the sample space of the random process, and each circle represents an event.

Intersection

The event “A and B” is called ______ of events A and B. It consists of all the outcomes in the sample space that are common to both events,
and is denoted A ∩ B.

Union

The event “A or B” is called the ___ of events A and B. It consists of all outcomes in the sample space that are in event A, event B, and is denoted A ∪ B.

conditional probability

The probability that one event happens given that another event is known to have happened is called a ___.

P(A|B)

the conditional probability that event A happens given that event B has happened is denoted by ___.

Conditional Probability Formula

P(A|B) = P(A and B)/P(B) = P(both events occur)/P(given event occurs)

independent events

A and B are ___ if knowing whether or not one event has happened does not changes the probability that the other event will happen. In other words, A and B are independent if P(A|B) = P(A|BC) = P(A) or if P(B|A) = P(B|AC) = P(B)

General Multiplication Rule

For any random process, the probability that events A and B both occur can be found using this rule: P(A and B) = P(A ∩ B) = P(A) * P(B}A)

tree diagram

shows the sample space of a random process involving multiple stages. The probability of each outcome is shown on the corresponding branch of the tree. All probabilities after the first stage are conditional probabilities.

Multiplication Rule for Independent Events

says that if A and B are independent events, the probability that A and B both occur is P(A and B) = P(A ∩ B) = P(A) * P(B)