STAT-100Q: Probability

Probability

Using the population information to infer the probable nature of the sample

Random Experiment

An act or process of observation that leads to a single outcome that cannot be predicted with certainty

Sample Point

The most basic outcome of an experiment (Such as an ordered pair, etc, (H, T))

Sample Space

A collection of ALL sample points of an experiment (The entire set of ordered pairs)

Event

A specific collection of sample points

Simple Event

Contains only one sample point

Compound Event

The composition of two or more other events (Contains two or more sample points)

Permutation

An ordered arrangement of items where the order of the items is important

Combination

Interest in the number of selections from a sample where order is not important

∪

A union represents two events that both occur on a single performance of an experiment

∩

An intersection represents the area that two events have in common

Complimentary Event

The opposite event in a set of two mutually exclusive and collectively exhaustive outcomes

Additive Rule

The probability of the union of events A and B is the sum of the probabilities of events A and B minus the probability of the intersection of events A and B

Mutually Exclusive Events

A ∩ B contains no sample points; that is, if A and B have no sample points in common

Collectively Exhaustive Events

A set of events where at least one of the events must occur

Conditional Probability

Refers to the probability of an event A when additional information about the event B is given

Multiplicative Rule

Allows us to calculate the probability of the intersection of events when the conditional probability is known

Independent Events

Two events where one event does not alter the probability that the other events occur

Baye's Rule

When we are given information regarding the probability of an event A given that event B occurred (but we are really interested in knowing the probability that event B occurs given that A occurred)

Tree Diagrams

A diagram that maps out all possible outcomes of a series of events or decisions in a branching structure

Venn Diagrams

A diagram using overlapping circles to represent relationships between sets of data, showing how they share commonalities

P(A)

The probability of event A occuring

P(A | B)

The conditional probability of event A occurring, given that event B has already occurred

P(A U B)

The probability that event A or event B (or both) occur in a single performance

𝑃 (𝐴 ∩ 𝐵)

The probability of the intersection of two events occurring simultaneously

𝑃 (𝐴^c)

The probability of the complement of event A occurring, which is the probability that event A does not happen