Mathematics · Probability

Min-Entropy from Maximum Probability maximum outcome probability Solver

Rearrange the min-entropy from maximum probability relationship and solve for maximum outcome probability.

Runs locally
Your numbers

Inputs and results stay in this browser. Change one value at a time to explore the relationship.

Your inputCalculatedPassed forward in chains
maximum outcome probability0.125
Reconstructed min-entropy in nats2.079442

Calculation steps

  1. Use b=e^(−c/a) with min-entropy in nats=2.0794415416798357 and logarithm unit scale=1.
  2. maximum outcome probability=0.12500000000000003.
  3. Substitution into c=−a ln(b) reconstructs 2.0794415416798357.

Understand Min-Entropy from Maximum Probability: solve maximum outcome probability

One idea, three depths

Choose how deeply to explain Min-Entropy from Maximum Probability: solve maximum outcome probability

Min-Entropy from Maximum Probability: solve maximum outcome probability: Rearrange the min-entropy from maximum probability relationship and solve for maximum outcome probability.

Age 5Explain it to a 5-year-oldStart with a picture

Imagine using Min-Entropy from Maximum Probability: solve maximum outcome probability to answer this question: rearrange the min-entropy from maximum probability relationship and solve for maximum outcome probability? Enter min-entropy in nats and logarithm unit scale; the calculator shows maximum outcome probability. For example: logarithm unit scale=1 and maximum outcome probability=0.125 produce min-entropy in nats=2.0794415416798357. The answer tells you maximum outcome probability.

Age 15Explain it to a 15-year-oldConnect it to the formula

Min-entropy is the negative natural logarithm of the largest outcome probability when the unit scale is one. This page isolates maximum outcome probability and verifies it in the original relationship. The rule is b=e^(−c/a). Its input values are min-entropy in nats, logarithm unit scale, and the main result is maximum outcome probability. For example: logarithm unit scale=1 and maximum outcome probability=0.125 produce min-entropy in nats=2.0794415416798357.

CollegeExplain it at college levelState the model precisely

This calculator evaluates the stated min-entropy from maximum probability: solve maximum outcome probability relation over the valid real-number domain stated below. The implemented relation is b=e^(−c/a), evaluated from min-entropy in nats, logarithm unit scale to produce maximum outcome probability. Min-entropy is the negative natural logarithm of the largest outcome probability when the unit scale is one. This page isolates maximum outcome probability and verifies it in the original relationship. For bits, divide the natural-log result by ln two or use a base-two convention.

Inputs and valid domain

  • min-entropy in nats must be a finite real number.
  • logarithm unit scale must be a finite real number.

Important boundary: For bits, divide the natural-log result by ln two or use a base-two convention.

The formula

b=e^(−c/a)

How the calculator works through it

It substitutes min-entropy in nats, logarithm unit scale into the formula and exposes every numerical step above. The main output is maximum outcome probability, accompanied by Reconstructed min-entropy in nats.

Read the result correctly

The maximum outcome probability is the direct answer to “rearrange the min-entropy from maximum probability relationship and solve for maximum outcome probability.” Read it with the units shown beside the inputs; a sign, angle, percentage or rate changes what the number means.

A worked check

logarithm unit scale=1 and maximum outcome probability=0.125 produce min-entropy in nats=2.0794415416798357.

Where this model stops being reliable

For bits, divide the natural-log result by ln two or use a base-two convention.

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 Min-Entropy from Maximum Probability: solve maximum outcome probability works. They never block the calculator, and “optional” means useful context rather than a hidden requirement.

Hard requirements

  • Reading formulas and substituting values

    Min-Entropy from Maximum Probability: solve maximum outcome probability uses b=e^(−c/a). 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 Min-Entropy from Maximum Probability: solve maximum outcome probability result says about possible outcomes.

    Review this foundation about 5 min

Optional enrichment

  • Ordered arrangements

    Counting ordered arrangements can extend Min-Entropy from Maximum Probability: solve maximum outcome probability to more detailed sample spaces and event models.

    Review this foundation about 5 min
Learn the missing foundationsI already know these — show the code

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

  1. Read min-entropy in nats, logarithm unit scale.
  2. Evaluate the principal relationship: b=e^(−c/a).
  3. Return maximum outcome probability and check the domain conditions described above.
Python
            from math import *

def min_entropy_from_maximum_probability_solve_b(c, a) -> float:
    return exp((-(c / a)))

assert abs(min_entropy_from_maximum_probability_solve_b(2.0794415416798357, 1) - 0.12500000000000003) < 1e-6 * max(1.0, abs(0.12500000000000003))
          
Current calculator valuesUpdates when you change an input above.
              
            
C
            #include <assert.h>
#include <math.h>

double min_entropy_from_maximum_probability_solve_b(double c, double a) {
    return exp((-(c / a)));
}

int main(void) {
    const double expected = 0.12500000000000003;
    const double actual = min_entropy_from_maximum_probability_solve_b(2.0794415416798357, 1);
    assert(fabs(actual - expected) < 1e-6 * fmax(1.0, fabs(expected)));
}
          
Current calculator valuesUpdates when you change an input above.
              
            
C++
            #include <cassert>
#include <cmath>
#include <numbers>

double min_entropy_from_maximum_probability_solve_b(double c, double a) {
    return std::exp((-(c / a)));
}

int main() {
    constexpr double expected = 0.12500000000000003;
    const double actual = min_entropy_from_maximum_probability_solve_b(2.0794415416798357, 1);
    assert(std::fabs(actual - expected) < 1e-6 * std::fmax(1.0, std::fabs(expected)));
}
          
Current calculator valuesUpdates when you change an input above.
              
            
Linux x86-64 assembly

x86-64 NASM · System V ABI · Linux · SSE2 with libm where required

            ; double min_entropy_from_maximum_probability_solve_b(double c, double a)
; Linux x86-64 NASM · System V ABI · first eight doubles in xmm0–xmm7
extern exp
global min_entropy_from_maximum_probability_solve_b
section .text

min_entropy_from_maximum_probability_solve_b:
    push rbp
    mov rbp, rsp
    sub rsp, 48
    movsd [rbp-8], xmm0
    movsd [rbp-16], xmm1
    movsd xmm0, [rbp-8]
    divsd xmm0, [rbp-16]
    movsd [rbp-40], xmm0
    pxor xmm0, xmm0
    subsd xmm0, [rbp-40]
    movsd [rbp-32], xmm0
    movsd xmm0, [rbp-32]
    call exp wrt ..plt
    movsd [rbp-24], xmm0
    movsd xmm0, [rbp-24]
    leave
    ret
          
Current calculator valuesUpdates when you change an input above.
              
            
MATLAB
            function result = min_entropy_from_maximum_probability_solve_b(c, a)
    result = exp((-(c / a)));
end
          
Current calculator valuesUpdates when you change an input above.
              
            
Wolfram Language
            ClearAll[mwCalculate];
mwCalculate[c_, a_] := Exp[(-(c / a))];
          
Current calculator valuesUpdates when you change an input above.
              
            

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 textbook
Cite 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). Min-Entropy from Maximum Probability maximum outcome probability Solver. MW SysArc Tools. https://math.mwsysarc.com/probability/min-entropy-from-maximum-probability-maximum-outcome-probability-solver

MLA 9

MW SysArc. “Min-Entropy from Maximum Probability maximum outcome probability Solver.” MW SysArc Tools, 21 July 2026, https://math.mwsysarc.com/probability/min-entropy-from-maximum-probability-maximum-outcome-probability-solver. Accessed 31 Aug. 2026.

Chicago 17

MW SysArc. “Min-Entropy from Maximum Probability maximum outcome probability Solver.” MW SysArc Tools. Published July 21, 2026. Accessed August 31, 2026. https://math.mwsysarc.com/probability/min-entropy-from-maximum-probability-maximum-outcome-probability-solver.

Harvard

MW SysArc (2026) ‘Min-Entropy from Maximum Probability maximum outcome probability Solver’, MW SysArc Tools. Published 21 July 2026. Available at: https://math.mwsysarc.com/probability/min-entropy-from-maximum-probability-maximum-outcome-probability-solver (Accessed: 31 August 2026).

BibTeX and RIS records

BibTeX

@misc{mwsysarc_min_entropy_from_maximum_probability_solve_b_2026,
  author = {{MW SysArc}},
  title = {Min-Entropy from Maximum Probability maximum outcome probability Solver},
  howpublished = {MW SysArc Tools},
  year = {2026},
  url = {https://math.mwsysarc.com/probability/min-entropy-from-maximum-probability-maximum-outcome-probability-solver},
  note = {Published July 21, 2026; accessed August 31, 2026}
}

RIS

TY  - ELEC
AU  - MW SysArc
TI  - Min-Entropy from Maximum Probability maximum outcome probability Solver
T2  - MW SysArc Tools
PY  - 2026
DA  - 2026-07-21
Y2  - 2026-08-31
UR  - https://math.mwsysarc.com/probability/min-entropy-from-maximum-probability-maximum-outcome-probability-solver
N1  - Published July 21, 2026
ER  -

Clear answers

Frequently asked questions

What does the Min-Entropy from Maximum Probability: solve maximum outcome probability do?

Rearrange the min-entropy from maximum probability relationship and solve for maximum outcome probability.

How does the Min-Entropy from Maximum Probability: solve maximum outcome probability work?

The calculator applies b=e^(−c/a). Min-entropy is the negative natural logarithm of the largest outcome probability when the unit scale is one. This page isolates maximum outcome probability and verifies it in the original relationship.

What can I learn from the Min-Entropy from Maximum Probability: solve maximum outcome probability?

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 .

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