AMTH 108 Quiz 1 Notes

Union

A∪B denotes the combination of both sets A and B, representing outcomes that are in A, in B, or in both.

Intersection

A∩B signifies the outcomes common to both sets A and B, indicating where both overlap.

Complement

A^c denotes the outcomes not in set A.

Empty set

The notation ∅ represents a set that contains no elements.

Multiplication Principle

The total number of possible outcomes is the product of possible outcomes from each individual event.

Permutations

The arrangement of items in a specific order; calculated as nPk=n!/(n−k)!. Used when order matters.

Combinations

The selection of items without regard to order; calculated as nCk=n!/(k!(n−k)!). Used when order does not matter.

Probability Basics

Refers to the range of a probability P(E) from 0 to 1, where P(∅) equals 0 and P(X) equals 1.

Equally likely outcomes

The probability P(E) is calculated as the number of favorable outcomes divided by the total number of outcomes.

Complements

The probability of the complement event P(Ec) is calculated as 1 - P(E).

Two-Event Probability

The formula P(A∪B)=P(A)+P(B)−P(A∩B) calculates the probability of at least one of two events occurring.

Three-Event Inclusion–Exclusion

Describes the probability of three events A, B, and C, calculated using their individual probabilities and their intersections.

Venn Diagrams

Visual representations used to illustrate set relationships, where all regions should sum to 1.

Conditional Probability

P(E|A) represents the probability of event E occurring given that event A has occurred, adjusting the sample space accordingly.

Independence

Events A and B are independent if P(A∩B)=P(A)P(B) and P(A|B)=P(A).