Mathematics · Probability
Independent Event Union Calculator
Calculate probability of a or b from probability of a and probability of b.
Inputs and results stay in this browser. Change one value at a time to explore the relationship.
Calculation steps
- Use c=a+b−ab with probability of A=0.3 and probability of B=0.4.
- probability of A or B=0.58.
Understand Independent Event Union
One idea, three depths
Choose how deeply to explain Independent Event Union
Independent Event Union: Calculate probability of a or b from probability of a and probability of b.
Age 5Explain it to a 5-year-oldStart with a picture
Imagine using Independent Event Union to answer this question: calculate probability of a or b from probability of a and probability of b? Enter probability of A and probability of B; the calculator shows probability of A or B. For example: probability of A=0.3 and probability of B=0.4 produce probability of A or B=0.58. The answer tells you probability of A or B.
Age 15Explain it to a 15-year-oldConnect it to the formula
For independent events, subtracting the overlap ab prevents double counting. This page evaluates the relationship directly. The rule is c=a+b−ab. Its input values are probability of A, probability of B, and the main result is probability of A or B. For example: probability of A=0.3 and probability of B=0.4 produce probability of A or B=0.58.
CollegeExplain it at college levelState the model precisely
This calculator evaluates the stated independent event union relation over the valid real-number domain stated below. The implemented relation is c=a+b−ab, evaluated from probability of A, probability of B to produce probability of A or B. For independent events, subtracting the overlap ab prevents double counting. This page evaluates the relationship directly. Enter probabilities as decimals and use this form only when independence is justified.
Inputs and valid domain
- probability of A must be a finite real number.
- probability of B must be a finite real number.
Important boundary: Enter probabilities as decimals and use this form only when independence is justified.
The formula
c=a+b−ab
How the calculator works through it
It substitutes probability of A, probability of B into the formula and exposes every numerical step above. The main output is probability of A or B.
Read the result correctly
The probability of A or B is the direct answer to “calculate probability of a or b from probability of a and probability of b.” Read it with the units shown beside the inputs; a sign, angle, percentage or rate changes what the number means.
A worked check
probability of A=0.3 and probability of B=0.4 produce probability of A or B=0.58.
Where this model stops being reliable
Enter probabilities as decimals and use this form only when independence is justified.
Learn it by changing one value
Begin with the worked example, then change one value while keeping the others fixed. Compare the new result and calculation steps to identify which part of the formula changed.
Dictionary terms behind this calculator
Before studying the codeWhat you should know firstUse the calculator immediately, or check the foundations before reading the implementation.
These foundations help you understand why Independent Event Union works. They never block the calculator, and “optional” means useful context rather than a hidden requirement.
Hard requirements
- Reading formulas and substituting values
Independent Event Union uses c=a+b−ab. You need to recognise what each side represents before substituting the stated inputs or rearranging the relationship.
Review this foundation about 4 min
Strong support
- Probability as a modelled proportion
Probability rules are needed to interpret what the Independent Event Union result says about possible outcomes.
Review this foundation about 5 min
Optional enrichment
- Ordered arrangements
Counting ordered arrangements can extend Independent Event Union to more detailed sample spaces and event models.
Review this foundation about 5 min
Mathematics → algorithm → program
Implement this calculation in code
These are direct reference implementations of the calculator's principal relationship and first output. They run locally and include a small known-answer check where the language supports it.
Algorithm
- Read probability of A, probability of B.
- Evaluate the principal relationship: c=a+b−ab.
- Return probability of A or B and check the domain conditions described above.
Python
from math import *
def independent_event_union_calculator(a, b) -> float:
return ((a + b) - (a * b))
assert abs(independent_event_union_calculator(0.3, 0.4) - 0.58) < 1e-6 * max(1.0, abs(0.58))
C
#include <assert.h>
#include <math.h>
double independent_event_union_calculator(double a, double b) {
return ((a + b) - (a * b));
}
int main(void) {
const double expected = 0.58;
const double actual = independent_event_union_calculator(0.3, 0.4);
assert(fabs(actual - expected) < 1e-6 * fmax(1.0, fabs(expected)));
}
C++
#include <cassert>
#include <cmath>
#include <numbers>
double independent_event_union_calculator(double a, double b) {
return ((a + b) - (a * b));
}
int main() {
constexpr double expected = 0.58;
const double actual = independent_event_union_calculator(0.3, 0.4);
assert(std::fabs(actual - expected) < 1e-6 * std::fmax(1.0, std::fabs(expected)));
}
Linux x86-64 assembly
x86-64 NASM · System V ABI · Linux · SSE2 with libm where required
; double independent_event_union_calculator(double a, double b)
; Linux x86-64 NASM · System V ABI · first eight doubles in xmm0–xmm7
global independent_event_union_calculator
section .text
independent_event_union_calculator:
push rbp
mov rbp, rsp
sub rsp, 48
movsd [rbp-8], xmm0
movsd [rbp-16], xmm1
movsd xmm0, [rbp-8]
addsd xmm0, [rbp-16]
movsd [rbp-32], xmm0
movsd xmm0, [rbp-8]
mulsd xmm0, [rbp-16]
movsd [rbp-40], xmm0
movsd xmm0, [rbp-32]
subsd xmm0, [rbp-40]
movsd [rbp-24], xmm0
movsd xmm0, [rbp-24]
leave
ret
MATLAB
function result = independent_event_union_calculator(a, b)
result = ((a + b) - (a * b));
end
Wolfram Language
ClearAll[mwCalculate];
mwCalculate[a_, b_] := ((a + b) - (a * b));
Continue in mathematical software
The downloaded file includes your current inputs and first calculated result. It is created locally.
Floating-point answers can differ slightly by language, compiler and processor. Compare within a suitable tolerance rather than assuming every decimal representation will be identical.
Supporting sourcesAcademic referencesPrimary standards, textbooks and complete citations
Standards, reading and academic references
Use the calculator as the worked interaction, then consult the primary standards and academic textbooks listed below. MW SysArc links to the original sources; the explanation on this page is original and does not reproduce them.
Introductory Statistics 2e
Read the free OpenStax statistics textbookCite this book
- APA 7
- Illowsky, B., & Dean, S. (2023). Introductory statistics 2e. OpenStax. https://openstax.org/books/introductory-statistics-2e/pages/1-introduction
- MLA 9
- Illowsky, Barbara, and Susan Dean. Introductory Statistics 2e. OpenStax, 2023, https://openstax.org/books/introductory-statistics-2e/pages/1-introduction.
- Chicago author-date
- Illowsky, Barbara, and Susan Dean. 2023. Introductory Statistics 2e. Houston, TX: OpenStax. https://openstax.org/books/introductory-statistics-2e/pages/1-introduction.
OpenStax entries are free to read online. Follow the licence shown on each linked source before redistributing or adapting its content.
Reuse the page responsiblyCite this pageAPA, MLA, Chicago, Harvard, BibTeX and RIS
These formats cite this calculator page itself. They are separate from the academic references above, which support the mathematical method and terminology.
APA 7
MW SysArc. (2026, July 21). Independent Event Union Calculator. MW SysArc Tools. https://math.mwsysarc.com/probability/independent-event-union-calculator
MLA 9
MW SysArc. “Independent Event Union Calculator.” MW SysArc Tools, 21 July 2026, https://math.mwsysarc.com/probability/independent-event-union-calculator. Accessed 31 Aug. 2026.
Chicago 17
MW SysArc. “Independent Event Union Calculator.” MW SysArc Tools. Published July 21, 2026. Accessed August 31, 2026. https://math.mwsysarc.com/probability/independent-event-union-calculator.
Harvard
MW SysArc (2026) ‘Independent Event Union Calculator’, MW SysArc Tools. Published 21 July 2026. Available at: https://math.mwsysarc.com/probability/independent-event-union-calculator (Accessed: 31 August 2026).
BibTeX and RIS records
BibTeX
@misc{mwsysarc_independent_event_union_calculator_2026,
author = {{MW SysArc}},
title = {Independent Event Union Calculator},
howpublished = {MW SysArc Tools},
year = {2026},
url = {https://math.mwsysarc.com/probability/independent-event-union-calculator},
note = {Published July 21, 2026; accessed August 31, 2026}
}RIS
TY - ELEC
AU - MW SysArc
TI - Independent Event Union Calculator
T2 - MW SysArc Tools
PY - 2026
DA - 2026-07-21
Y2 - 2026-08-31
UR - https://math.mwsysarc.com/probability/independent-event-union-calculator
N1 - Published July 21, 2026
ER -Clear answers
Frequently asked questions
What does the Independent Event Union do?
Calculate probability of a or b from probability of a and probability of b.
How does the Independent Event Union work?
The calculator applies c=a+b−ab. For independent events, subtracting the overlap ab prevents double counting. This page evaluates the relationship directly.
What can I learn from the Independent Event Union?
It connects the mathematical rule to your chosen numbers and shows each calculation step. Change one input at a time to see how the result responds.
Does MW SysArc receive or store what I enter?
No. The calculation runs locally in your browser. MW SysArc does not receive or store your calculation inputs.
How should I use the result?
Use the steps to understand the method, then verify important school or professional work using the notation and rounding rules required in your setting.
Last reviewed . Calculations tested .