Exam P Study Set #1 - General Probability

Element

possible outcome of an experiment (ex. flipping a coin, heads/tails are the elements)

Set

a collection of zero or more elements. a set is denoted with uppercase letter (Set A consists of elements x, y, z)

Venn Diagram

also known as the set diagram, is a diagram showing the relationship between a finite number of sets. also useful for illustrating probabilities and events

Sample Space

collection of all possible outcomes. it is usually denoted by uppercase S. (ex. S = {heads/tails} is the sample space for a coin flip)

Empty Set

a set containing zero elements

Event

a subset of the sample space. events and sets are interchangeable, where an event is usually described in words (ex. “coin flip result is a heads”)

Subset

A set that contains elements that are all in another set. (ex. Set D is a subset of set E, because all of the elements in D are also in E.)

Union

the _____ of multiple sets is the set of elements that are contained in at least one of the sets. Typically common around the term “or”. (ex. F = {1, 2, 3} and G = {3, 4, 5}, the _____ is {1, 2, 3, 4, 5}).

Intersection

the set of elements that are common for multiple sets (ex. F = {1, 2, 3} and G = {3, 4, 5}, the ____ is {3}

Difference

the set containing all the elements in one set but not the other (ex. F = {1, 2, 3} and G = {3, 4, 5}, F - G = {1, 2}, G - F = {4, 5})

Mutually Exclusive

two sets who share no common elements

Disjoint

same meaning as mutually exclusive

Complement

the ______ of set T is the set containing all of the elements in the sample space, except the elements that are in T. a set and its complement are mutually exclusive by definition

Probability

measures the likelihood of an outcome.

What numbers are probabilities defined between?

0 and 1

What is the probability of an empty set?

0

What is the probability of a sample space?

1

Additive Law of Probability

Pr(A U B) = Pr(A) + Pr(B) - Pr(A intersect B) *assumes A and B in sample space