**Home** / **probability sample space calculator** / Basic Probability Formulas - NASA

Basic Probability Formulas

Complementary events: The complement of event A is everything not in A. Complementary events are mutually

exclusive events and together make up the sample space. The probability of the sample space is one.

Independent events: The occurrence of any one of the events does not affect the probabilities of the occurrences

of the other events. Events A and B are independent if probability of A given B equals probability of A.

Dependent events (or non-independent events): Events that are not independent, i.e., P(A given B) P(A).

Mutually exclusive events (or disjoint events): If event A occurs, then event B cannot occur, and conversely.

De Morgan's Rule (one form): Via a double complement, A or B = (Ac and Bc)c = "not [ (not A) and (not B) ]". For

example, "I want A, B, or both to work" (Reliability) equates to "I do not want both A and B not to work" (Safety).

Event Details Formula (from English to mathematical operations)

A Probability of A, P(A) P(A) is at or between zero and one: 0 P(A) 1

not A, Ac Ac is the complement of A Probability of not A = P(Ac) = 1 - P(A)

A and B are independent

events P(A and B) = P(A)*P(B)

A and B A and B are dependent

events P(A and B) = P(A)*P(B | A) = P(B)*P(A | B) as 2 forms

A and B are mutually

exclusive events P(A and B) = 0

A and B are independent P(A or B) = P(A) + P(B) - P(A)*P(B) conveniently expands to

events = 1 - [1 - P(A)]*[1 - P(B)] or is obtained from De Morgan's Rule

A or B A and B are dependent

events P(A or B) = P(A) + P(B) - P(A)*P(B | A) as 1 of 2 forms

A and B are mutually

exclusive events P(A or B) = P(A) + P(B)

A given B, Conditional: outcome of A P(A given B) = P(A | B) = P(A)*P(B | A) / P(B) [Bayes' Thm]

A | B given B has occurred To make this formula, solve the 2 forms in "A and B" for P(A | B)

210624 Tim.Adams@NASA.gov

What does probability space mean?In short, a probability space is a measure space such that the measure of the whole space is equal to one. . . Probabilities can be ascribed to points of . All subsets of

Title:

Subject:

Keywords:

Author: Adams, Timothy C. (KSC-NETA0)

Creator: Acrobat PDFMaker 17 for Word

Producer: Adobe PDF Library 17.11.238

CreationDate: Mon Jun 28 15:52:15 2021

ModDate: Mon Jun 28 15:59:25 2021

Tagged: yes

Form: AcroForm

Pages: 1

Encrypted: no

Page size: 612 x 792 pts (letter) (rotated 0 degrees)

File size: 137762 bytes

Optimized: no

PDF version: 1.6